MICROSCOPY WITH STRUCTURED PLANE ILLUMINATION AND POINT ACCUMULATION FOR IMAGING AND NANOSCALE TOPOGRAPHY

[0001] This application is a non-provisional of, and claims priority under 35 U.S.C. §119 to, U.S. Provisional Patent Application No. 62/088,593, filed Dec. 6, 2014, entitled “MICROSCOPY WITH LATTICE LIGHT SHEETS AND POINT ACCUMULATION FOR IMAGING AND NANOSCALE TOPOGRAPHY,” and U.S. Provisional Patent Application No. 62/088,681, filed Dec. 7, 2014, entitled “MICROSCOPY WITH LATTICE LIGHT SHEETS AND POINT ACCUMULATION FOR IMAGING AND NANOSCALE TOPOGRAPHY,” to the disclosure of both of which is incorporated herein in their entireties.

[0002] Several imaging technologies are commonly used to interrogate biological systems. Widefield imaging floods the specimen with light, and collects light from the entire specimen simultaneously, although high resolution information is only obtained from that portion of the sample close to the focal plane of the imaging objective lens. Confocal microscopy uses the objective lens to focus light within the specimen, and a pinhole in a corresponding image plane to pass to the detector only that light collected in the vicinity of the focus. The resulting images exhibit less out-of-focus background information on thick samples than is the case in widefield microscopy, but at the cost of slower speed, due to the requirement to scan the focus across the entire plane of interest.

[0003] In a first general aspect, a method includes: bathing a sample in a first solution, where the solution includes first labels that have a binding affinity for a first structure on or within the sample and that emit light in response to excitation light; (b) providing a sheet of excitation light to the sample, where the sheet of excitation light has a FWHM thickness; (c) imaging onto a detector light emitted from labels bound to the structure in response to light provided by the sheet of excitation light, where the light is imaged with a detection objective that has a depth of focus that is comparable to or greater than the FWHM thickness and where an optical axis of the detection objective is substantially perpendicular to the sheet of excitation light; (d) controlling the bathing of the sample with the solution that includes the labels and the imaging of the light emitted from the bound labels, such that the imaged light from different individual labels bound to the structure is resolved on the detector. Steps (b)-(d) are repeated to image, at different times, light from labels bound to the structure at different locations on or within the sample.

[0004] In another general aspect, an apparatus includes a solution configured to bath a sample, the solution including first labels that have a binding affinity for a first structure on or within the sample and that emit light in response to excitation light. The apparatus includes a first light source of excitation light and first optical elements configured for providing the excitation light to the sample in a sheet of excitation light having a FWHM thickness. The apparatus includes a detector configured for recording images of light emitted from the sample in response to the sheet of excitation light and a a detection objective that has a depth of focus that is comparable to or greater than the FWHM thickness and that is configured for imaging onto the detector light emitted from labels bound to the structure in response to the provided sheet of excitation light. An optical axis of the detection objective is substantially perpendicular to the sheet of excitation light. The apparatus further includes at least one processor configured for controlling the imaging of the light emitted from the bound labels, such that the imaged light from different individual labels bound to the structure is resolved on the detector. The at least one processor is also configured for controlling the first light source, the optical elements and the detector to image, at different times, light from labels bound to the structure at different locations on or within the sample.

[0005] The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims.

[0054] Like reference numerals in the different figures describe like elements in the different figures.

[0055] For biological imaging, a powerful imaging modality is fluorescence, since specific sub-cellular features of interest can be singled out for study by attaching fluorescent labels to one or more of their constituent proteins. Both widefield and confocal microscopy can take advantage of fluorescence contrast. One limitation of fluorescence imaging, however, is that fluorescent molecules can be optically excited for only a limited period of time before they are permanently extinguished (i.e., “photobleach”). Not only does such bleaching limit the amount of information that can be extracted from the specimen, it can also contribute to photo-induced changes in specimen behavior, phototoxicity, or even cell death.

[0056] Unfortunately, both widefield and confocal microscopy excite fluorescence in every plane of the specimen, whereas the information rich, high resolution content comes only from the vicinity of the focal plane. Thus, both widefield and confocal microscopy are very wasteful of the overall fluorescence budget and potentially quite damaging to live specimens. A third approach, two photon fluorescence excitation (TPFE) microscopy, uses a nonlinear excitation process, proportional to the square of the incident light intensity, to restrict excitation to regions near the focus of the imaging objective. However, like confocal microscopy, TPFE requires scanning this focus to generate a complete image. Furthermore, the high intensities required for TPFE can give rise to other, nonlinear mechanisms of photodamage in addition to those present in the linear methods of widefield and confocal microscopy.

[0057] Localization microscopy (e.g., photo activation localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM), and point accumulation imaging in nanoscale topography (PAINT)) has enabled the imaging of biological samples at resolutions that can exceed the diffraction limit by several orders of magnitude. However, despite their ability to localize fluorescent molecules in both two and three-dimensions, many applications of localization microscopy have focused on the ventral surface or very thin (less than one micron) lamellar regions of adherent cells. Two challenges arise when extending localization microscopy into thicker three-dimensional (3D) samples. First, in order to localize single molecules, background signal from fluorescent emitters residing outside of the focal plane must be reduced either by limiting the excitation volume or by restricting the thickness of the specimen. Confinement at sub 100 nm length scales can be achieved through total internal reflection fluorescence (TIRF) microscopy or by mechanical sectioning of larger samples. However, these strategies limit observations to immediately adjacent to the coverslip or remove the structure of interest from its native 3D context. At larger length scales high localization precision can be obtained in thick samples, but the region that is exposed to activation and/or excitation radiation is generally thicker than the depth of focus of the detection optics, leading to substantial out-of-focus background and premature bleaching of activated molecules.

[0058] In addition, an often overlooked challenge for high-resolution 3D structural imaging is that the number of molecules required to adequately sample a given spatial frequency, and thus resolve a structure of a given size, scales exponentially with the spatial dimension in which those structures are imaged. This relationship intimately links optical resolution, labeling density, and spatial dimension in localization microscopy.

[0059] Localization-microscopy-generated images are different from images by other fluorescence methods. In most methods, the intensity of a pixel is proportional to the number of photons (which is generally proportional to the fluorophore density) emitted from a region of the sample after magnification and filtering by a spatially invariant microscope point spread function (PSF). The units in these traditional images (as well as more modern ones such as structured illumination and stimulated emission depletion microscopy) are then given as camera counts or, in some cases, photons. On the other hand, a localization microscopy image is usually displayed as a spatially summed distribution of 2D or 3D Gaussian spots, each with an intensity proportional to the probability that the associated detected molecule is centered at a given location. The pixel intensity in a localization microscopy image is thus a unitless probability distribution. Seen another way, a localization microscopy image reflects our estimation that the next molecule to be localized will occur in a given spatial region.

[0060] Many studies erroneously intermix localization precision and image resolution, but the localization precision of a single molecule does not take into account the fact that for structural imaging, the goal is to resolve the underlying probability distribution across the whole region of interest, which requires the sampling of very large numbers of molecules. A common metric to incorporate the dependence of image resolution on molecular density is derived from the Nyquist-Shannon sampling theorem. This states that the image resolution is limited to no better than twice the mean spacing of localized molecules in the final image. In other words, only features with spatial frequencies that are below 1/(2*spacing of imaged labels) can be resolved. Thus, the Nyquist resolution limit can be expressed as

$\mathrm{Nyquist}\mathrm{Resolution}\mathrm{Limit}=\frac{2}{{\left[\mathrm{localization}\mathrm{density}\right]}^{1/N}}$

where N=1, 2, or 3 is the spatial dimension in which the structure is being sampled. This equation is sufficient for cases when localization uncertainty is significantly smaller than the mean localization spacing, but when this is not the case, a heuristic argument has been proposed that the overall resolution can be estimated by the root sum of the mean localization variance and the mean localization spacing:

$n_i=\frac{N}{\sqrt{2\pi }\sigma }{}^{-\frac{{\left(x_i-x_c\right)}^2}{2{\sigma }^2}},$

[0061] However, the above Nyquist analogy is not strictly correct, because in its original formulation, the Nyquist-Shannon sampling theorem assumes that a “sample” of the underlying signal occurs at regular intervals and returns the value of the function at a specific time or location. In contrast, the localization of a single molecule in space is stochastic and does not reveal the underlying molecular density at that location. Rather, it represents an independent “event” drawn from a probability distribution that is proportional to the underlying molecular density. The task for localization microscopy then is to observe a sufficient number of localization events to resolve the underlying distribution,

[0062] Consequently, a limitation to current techniques is that although isolated single molecules can be localized very precisely (e.g., exceeding precisions of 10 nm perpendicular to, and 20 nm parallel to, the optical axis of the detection objective), to translate this localization precision into reconstructed image resolution, the structure of interest must be sampled at sufficiently high density (e.g., approximately twice the localization precision via Nyquist sampling). This, in turn, requires high levels of expression of signal-emitting labels (e.g., photoactivatable proteins (for PALM) or antibody labeling (for STORM)). For example, to achieve an isotropic resolution (i.e., in all directions relative to the optical axis) of 20 nm requires the localization of at least 37,500 unique molecules within a 3D (250×250×600 nm) diffraction limited volume. However, these densities of signal-emitting labels are rarely achievable due to a cell's inability to tolerate overexpression of a labeled protein in the presence of such a high number of for fluorescent proteins, or due to difficulties in histological labeling. In addition, even if such labeling densities could be achieved with conventional fluorescent proteins or antibodies while avoiding over-expression artifacts and maintaining labeling specificity, the on:off contrast ratio of the activated:non-activated fluorophore must still be over 40,000:1 in order to accurately localize the one activated molecule against the background of those remaining, even under perfect optical sectioning illumination. Moreover, because localizations represent a stochastic sampling of the underlying molecular distribution, adequately sampling a given spatial frequency with sufficient signal-to-noise can require an order of magnitude increase in the number of molecules compared to what is strictly required according to the Nyquist criterion.

[0063] As described herein, to address the challenge of imaging features within a relatively thick sample while avoiding noise from out-of-focus background fluorescence, the light that activates and/or excites emitting labels within the sample can be confined to a relatively thin sheet (e.g., less than or approximately 1.1 micron thick). The sheet(s) or light can be created, for example, using structured plane illumination microscopy techniques (e.g. lattice light sheet microscopy techniques). The thickness of the illuminated planes or light sheets can be comparable to the depth of focus of the detection objective of the microscopy system (e.g., a 1.1 numerical aperture (NA) detection objective) and can be substantially thinner than light sheet localization approaches using Gaussian beams. By reducing the thickness of the light sheet(s) to this extent, it is possible to eliminate large dim spots on the detector from out-of-focus molecules that are difficult to localize above background signal and often fall below the detection threshold of localization algorithms. Furthermore, far more molecules can be localized per acquisition step, because the proximity of the fluorescing molecules to the focal plane insures that their smaller emission spots on the detector are unlikely to overlap. In addition, for photoactivated localization microscopy (PALM), by providing the activation light as well as the excitation light in a thin sheet to the focal plane of the detection objective, premature photobleaching of activated fluorophores that do not contribute to the final image can be reduced, which improves localization accuracy and enables higher densities of molecules to be imaged simultaneously.

[0064] To address the second challenge of wanting to image thick 3D specimens that are densely labeled with localizable optical labels, without the problems described above, the illumination scheme using thin light sheets can be combined with point accumulation for imaging of nanoscale topography (PAINT) microscopy techniques, which utilizes freely diffusing small fluorescent molecules that exist in the imaging buffer (e.g., at pM-nM concentrations). In the raw images, contrast can be provided by changes in the diffusion rate of individual labels as they bind to and are stabilized by the underlying substrate: only bound molecules appear as stable bright puncta at 10 ms or slower acquisition rates and are thus localized, while unbound molecules diffuse too rapidly to appear as a bright point of light in the raw images. Pixel values in the super-resolved image are then proportional to the number of stable binding events in a given region. In comparison to localization microscopy methods that label the specimen prior to imaging, PAINT labels continually bind to the specimen throughout the imaging process, providing a continuous source of fluorescent molecules to label the structure. Label binding can occur concurrently with photobleaching and localization, thus avoiding the background signal that would normally be contributed from spontaneously activated molecules of finite duty cycle or nonzero off-state emission in conventional PALM or STORM techniques and thus permitting precise localization of bound molecules at extremely high densities. In some implementations, PAINT labels that selectively bind to either intracellular membranes or fluorgenically to DNA can be used to label specimens. Thus, this combination of confined planar illumination of the specimen, stochastic binding of PAINT labels to specimens, and novel chemical probes can be used to perform optical microscopy at high localization precision and high labeling density, in multiple colors, for thick samples.

[0065] FIG. 1 is a schematic diagram of a light sheet microscopy (LSM) system 100. As shown in FIG. 1, the LSM system 100 uses a beam-forming lens 102, external to imaging optics, which includes an objective 104, to illuminate the portion of a specimen in the vicinity of the focal plane 106 of the objective. In one implementation, the lens 102 that provides illumination or excitation light to the sample can include a cylindrical lens that focuses light in only one direction, thereby providing a beam of light 108 that creates a sheet of light co-incident with the objective focal plane 106. A detector 110 then records the signal generated across the entire illuminated plane of the specimen. Because the entire plane is illuminated at once, images can be obtained very rapidly.

[0066] In another implementation, termed Digital Laser Scanned Light Sheet Microscopy (DSLM), the lens 102 can be a circularly symmetric multi-element excitation lens (e.g., having a low numerical aperture (NA) objective) that corrects for optical aberrations (e.g., chromatic and spherical aberrations) that are prevalent in cylindrical lenses. The illumination beam 108 of light then is focused in two directions to form a pencil beam of light co-incident with the focal plane 106 of the imaging objective 104. The width of the pencil beam is proportional to the 1/NA of the excitation lens, whereas its length is proportional to 1/(NA)². Thus, by using the illumination lens 102 at sufficiently low NA (i.e., NA<<1), the pencil beam 108 of the excitation light can be made sufficiently long to encompass the entire length of the desired field of view (FOV). To cover the other direction defining the lateral width of the FOV, the pencil beam can be scanned across the focal plane (e.g., with a galvanometer, as in confocal microscopy) while the imaging detector 110 integrates the signal that is collected by the detection optics 112 as the beam sweeps out the entire FOV.

[0067] A principal limitation of these implementations is that, due to the diffraction of light, there is a tradeoff between the XY extent of the illumination across the focal plane of the imaging objective, and the thickness of the illumination in the Z direction perpendicular to this plane. In the coordinate system used in FIG. 1, the X direction is into the page, the Y direction is in the direction of the illumination beam, and the Z direction is in the direction in which imaged light is received from the specimen.

[0068] FIG. 2 is a schematic diagram of a profile 200 of a focused Gaussian beam of light (i.e., a beam have a transverse profile approximated by a Gaussian function). As shown in FIG. 2, illumination light 202 of wavelength, λ, that is focused to a minimum beam waist, 2w_o, within the specimen will diverge on either side of the focus, increasing in width by a factor of √{square root over (2)} in a distance of z_R=πw_o²/λ, the so-called Rayleigh range. Table 1 shows specific values of the relationship between the usable FOV, as defined by 2z_R, and the minimum thickness 2w_o of the illumination sheet, whether created by a cylindrical lens, or by scanning a pencil beam created by a low NA objective.

	TABLE 1
	2Wo(μm, for λ = 500 nm)	2ZR(μm, for λ = 500 nm)
	0.2	0.06
	0.4	0.25
	0.6	0.57
	0.8	1.00
	1.0	1.57
	2.0	6.28
	5.0	39.3
	10.0	157
	20.0	628

[0069] From Table 1 it can be seen that, to cover FOVs larger than a few microns (as would be required to image even small single cells in their entirety) the sheet thickness must be greater than the depth of focus of the imaging objective (typically, ˜1 micron). As a result, out-of-plane photobleaching and photodamage still remain (although less than in widefield or confocal microscopy, if the sheet thickness is less than the specimen thickness). Furthermore, the background from illumination outside the focal plane reduces contrast and introduces noise which can hinder the detection of small, weakly emitting objects. Finally, with only a single image, the Z positions of objects within the image cannot be determined to an accuracy better than the sheet thickness.

[0070] However, microscopy and imaging apparatus, systems, methods and techniques are described herein, which enable a light sheet or light beam to have a length that can be decoupled from its thickness, thus allowing the illumination of large fields of view (e.g., tens or even hundreds of microns) across a plane having a thickness on the order of, or smaller than, the depth of focus of the imaging objective. Such thin sheets and beams can be created, for example, by using illumination beams having a cross-sectional field distribution that is similar to a zeroth-order Bessel function or by using special spatially-structured light sheets. Such beams and sheets having a length that is decoupled from their thickness can be created by focusing light, not in a continuum of azimuthal directions across a cone, as is customary, but rather at a single azimuthal angle or range of azimuthal angles with respect to the axis of the focusing element and can overcome the limitations of the diffraction relationship shown in FIG. 2, because the relationship shown in FIG. 2 is only valid for lenses (cylindrical or objectives) that are uniformly illuminated. In some implementations, such a beam can be referred to as a Bessel beam or a Bessel-like beam.

[0071] FIG. 3 is a schematic diagram of a Bessel beam formed by an axicon 300. The axicon 300 is a conical optical element, which, when illuminated by an incoming plane wave 302 having an approximately-Gaussian intensity distribution in directions transverse to the beam axis, can form a Bessel beam 304 in a beam that exits the axicon.

[0072] FIG. 4 is a schematic diagram of a Bessel beam 400 formed by an annular apodization mask 402, where the annular mask 402 is illuminated to create a thin annulus of light at the back focal plane of a conventional lens 404. The mask 402 is separated from the lens 404 by the focal length, f. An angle, θ, can be defined as the inverse tangent of half the distance, d, from the center of the annular ring to a point within the ring divided by the focal length, where d_o can be used to denote the minimum diameter of the annular ring. Ideally, in either case shown by FIG. 3 or by FIG. 4, the axial wavevectors k_z of all rays converging to the focus are the same, and hence there is no variation of the beam along this direction. In practice, the finite diameter of the axicon 300, or the finite width, Δd, of the annular ring in the apodization mask 402 restricts the Bessel beam to a finite length. The optical system of the annular apodization mask 402 and the lens 404 can be characterized by a minimum and maximum numerical aperture, where the maximum numerical aperture is proportional to d_o+Δd, and the minimum numerical aperture is proportional to d_o. In other implementations, different optical elements, other than an axicon or an apodization mask, can be used to create an annulus of light. For example, a binary phase mask or a programmable spatial light modulator can be used to create the annulus of light.

[0073] FIG. 5 is a schematic diagram of a system 500 for Bessel beam light sheet microscopy. A light source 502 emits a light beam 504 that strikes an annular apodization mask 506. An annulus of excitation light 508 illuminates the back focal plane of microscope objective 510 to create an elongated Bessel beam 512 of light in a sample 514. By scanning this beam in a plane 516 transverse to the axis of the Bessel beam 512 and co-incident with the focal plane of a detection objective 504 while simultaneously integrating the collected signal 518 with a camera 520 located at a corresponding image plane of imaging optics 522, an image is obtained from a much thinner slice within the sample than is the case when either conventional light sheet microscopy or DSLM is used.

[0074] How much thinner the sheet of excitation light can be with Bessel beam illumination than with conventional light sheet microscopy or DSLM can be seen from a comparison of FIG. 6A, which shows a plot of the intensity profile of a Bessel beam, and FIG. 6B, which shows a plot of the intensity profile of a conventional beam. In the plots of FIGS. 5 and 6, Y is along the axis of the propagation direction of the beam, X is the direction of the excitation polarization (when linearly polarized light is used), and Z is along the axis of detection optics objective 522 and is orthogonal to X and Y. FIG. 7A is a plot of the intensity profile of a Bessel beam of FIG. 6A in the directions transverse to the propagation direction of the beam, and FIG. 7B is a plot of the Gaussian intensity profile of the conventional beam of FIG. 7A in the directions transverse to the propagation direction of the beam.

[0075] As seen in FIG. 6A, annular illumination across a small range of angles (θ=43 to 45 degrees) results in a Bessel-like beam approximately 50 wavelengths λ long in the Y direction, or roughly the same length obtained by conventional illumination using a plane wave having a Gaussian transverse intensity profile that is focused by a lens into an illumination beam having a cone half-angle of 12 degrees, as seen in FIG. 6B. However, the thickness of the Bessel-like beam is much narrower than the thickness of the conventional beam, yielding a much thinner sheet of excitation when scanned across a plane.

[0076] Furthermore, even longer Bessel-like beams can be made without compromising their cross-sectional width by restricting the annular illumination over an even smaller range of angles. FIG. 8A is a plot of an intensity profile in the YZ directions of a Bessel beam generated from an annular mask having a thinner annulus than is used to generate the intensity profile of the Bessel-like beam of FIG. 6A, and FIG. 8B is a plot of the transverse intensity profile for the beam in the XZ directions. As shown in FIG. 8A, annular illumination across a small range of angles (θ=44 to 45 degrees) results in in the YZ intensity profile of the Bessel-like beam shown in FIG. 8A, where the Bessel-like beam has a length of approximately 100 wavelengths in the Y direction. However, the transverse intensity profile of the longer Bessel beam is relatively unchanged compared with shorter Bessel beam, as can be seen from a comparison of FIG. 7A and FIG. 8B, and the thickness of the beam is not significantly greater than the thickness of the beam whose intensity profile is shown in FIG. 6A. In contrast, with conventional illumination the usual approach of lengthening the beam by reducing the NA results in an unavoidably larger diffraction limited cross-section, roughly in accordance with Table 1.

[0077] FIG. 9A is a schematic diagram of another system 900 for implementing thin light sheet microscopy. A collimated light 901, such as a laser beam having a Gaussian intensity profile, can be reflected from first galvanometer-type mirror 902 and then imaged by relay lens pair 903 and 904 onto a second galvanometer-type mirror 905 positioned at a point optically conjugate to the first galvanometer-type mirror 902. A second lens pair 906 and 907 then can relay the light to annular apodization mask 908 conjugate with the second galvanometer-type mirror 905. The annular light beam transmitted through this mask 908 then can be relayed by a third lens pair 910 and 911 onto a conjugate plane co-incident with the back focal plane of excitation objective 912. Finally, the annular light can be focused by objective 912 to form a Bessel-like beam 913 that is used to provide excitation light to a specimen.

[0078] The rotational axis of galvanometer mirror 902 can be positioned such that tilting this galvanometer-type mirror 902 causes the Bessel-like beam 913 to sweep across the focal plane of detection objective 915 (i.e., in the X direction), whose axis is orthogonal to (or whose axis has an orthogonal component to) the axis of the excitation objective 912. The signal light 914 can be directed by detection optics, including the detection objective 915, to a detection camera 917. The galvanometers-type mirrors 902, 905 can provide sweep rates of up to about 2 kHz, and with resonant galvanometer-type mirrors (e.g., Electro-Optical Products Corp, model SC-30) sweep rates can exceed 30 kHz. Extremely high frame rate imaging is then possible when the system is used in conjunction with a high frame rate detection camera (e.g., 500 frames/sec with an Andor iXon+DU-860 EMCCD, or >20,000 frames/sec with a Photron Fastcam SA-1 CMOS camera coupled to a Hamamatsu C10880-03 image intensifier/image booster).

[0079] The rotational axis of the galvanometer mirror 905 can be positioned such that tilting of this mirror causes the Bessel-like beam 913 to be translated along the axis of the detection objective 915. By doing so, different planes within a specimen can be accessed by the Bessel-like beam, and a three dimensional (3D) image of the specimen can be constructed, with much higher axial resolution than in conventional light sheet microscopy, due to the much narrower sheet of excitation afforded by Bessel-like excitation. In order to image each plane in focus, either detection objective 915 must be moved synchronously with the motion of the Bessel-like beam 913 imparted by the tilt of galvanometer-type mirror 905 (such as with a piezoelectric transducer (e.g., Physik Instrumente P-726)), or the effective plane of focus of the detection objective 915 must be altered, such as by using a second objective to create a perfect image of the sample. Of course, if 3D image stacks are not desired, the second galvanometer 905 and relay lenses 906 and 907 can be removed from the system shown in FIG. 9A, and the first galvanometer 902 and relay lenses 903 and 904 can be repositioned so that the apodization mask 908 is at a conjugate plane relative to galvanometer-type mirror 902. An acousto-optical tunable filter (AOTF) 918 can be used to block all excitation light from reaching the specimen when desired.

[0080] The system in FIG. 9A can be quite wasteful of the energy in light beam 901, because most of the light is blocked by apodization mask 908. If greater efficiency is desired, a diffractive optical element such as a binary phase mask or spatial light modulator and a collimating lens can be used to create an approximately annular light beam prior to more exact definition of this beam and removal of higher diffractive orders by the apodization mask 908.

[0081] In another implementation, shown in FIG. 9B, signal light 914 received by detection objective 915 can be transmitted through relay lenses 920, 922 and reflected off a galvanometer-type mirror 924 and then transmitted through relay lenses 926 and 928 and focused by a tube lens 930 onto a detector 932. An aperture mask (e.g., an adjustable slit) 934 can be placed at a focal plane of lens 926, and when the mask defines a slit the width of the slit 934 can be selected to block signal light from positions in the sample corresponding to side lobes of the Bessel-like beam illumination light, while passing signal light from positions in the sample corresponding to the central peak of the Bessel-like beam illumination light. The galvanometer-type mirror 924 can be rotated in conjunction with galvanometer-type mirror 902, so that when the Bessel-like beam is scanned in the X direction within the sample signal light from different positions within the sample passes through the slit 934.

[0082] Bessel-like beams can include excitation intensity in rings other than the central excitation maximum, which are evident in FIGS. 7A and 8B, and substantial energy can reside in the side lobes of a Bessel-like beam. Indeed, for an ideal Bessel beam of infinite extent, each side lobe contains energy equal to that in the central peak. Also, for an ideal Bessel beam, the ratio of the Rayleigh length of the beam to the minimum waist size of the beam is infinite. FIG. 10 shows a number of transverse intensity profiles for different Bessel-like beams. In FIG. 10, the first column shows theoretical two-dimensional intensity plots in the XZ plane, the second column shows experimental intensity plots in the third column shows a one-dimensional intensity profile at the X=0 plane. Different rows in FIG. 10 correspond to Bessel-like beams that are created using different annular apodization masks. Each row indicates the maximum and minimum numerical aperture of the annular ring of the mask. In the first row, the maximum numerical aperture is 0.80, and the minimum numerical aperture is 0.76. In the second row, the maximum numerical aperture is 0.60, and the minimum numerical aperture is 0.58. In a third row, the maximum numerical aperture is 0.53 and the minimum numerical aperture is 0.51. In the fourth row the maximum numerical aperture is 0.40, and the minimum numerical aperture is 0.38. In the fifth row, the maximum numerical aperture is 0.20, and the minimum numerical aperture is 0.18.

[0083] Because of the intensity in the side lobes, the integrated fluorescence excitation profile after the beam is swept in the X direction exhibits broad tails, as shown in FIG. 11. FIG. 11A shows the theoretical and experimental intensity profile in the Z direction of a Bessel-like beam, when the center of the beam is fixed at the X=0 and Z=0 plane, where experimental values are shown by dots and theoretical values are shown by solid lines. The intensity profile shown in FIG. 11A is representative of a Bessel-like beam formed from an annular apodization mask that generates an annulus of 488 nm light at a rear pupil of an excitation objective, where the annulus has a maximum numerical aperture of 0.60 and a minimum numerical aperture of 0.58. When this Bessel-like beam is swept in the X direction to create a sheet of excitation light centered on the Z=0 plane, integrated fluorescence excitation profile shown in FIG. 11B results because of the side lobes in the beam. Thus, the side lobes of the Bessel beam can contribute out-of-focus background fluorescence and premature photobleaching of the sample. A number of techniques can be used to mitigate the effect of these lobes.

[0084] Choosing a thicker annulus in the annular mask 506 suppresses these tails, but it does so at the expense of the length of the beam, as the beam becomes more Gaussian and less Bessel-like in character. This effect can be seen in FIG. 12A and FIG. 12B. FIG. 12A shows plots of the width of fluorescence excitation profiles of beams swept in the X direction in the Z=0 plane, where the beams that are swept are created from annuli that have different thicknesses. FIG. 12B shows plots of the axial intensity profiles (i.e., in the Y direction) of the beams that are swept. For each of the beams whose intensity profiles are plotted in FIG. 12A and FIG. 12B, the maximum numerical aperture is 0.60. A beam with an intensity profile 1202 has a minimum numerical aperture equal to 0.58. A beam with an intensity profile 1204 has a minimum numerical aperture equal to 0.56. A beam with an intensity profile 1206 has a minimum numerical aperture people equal to 0.52. The beam with an intensity profile 1208 has a minimum numerical aperture equal to 0.45. A beam with an intensity profile 1210 has a minimum numerical aperture equal to 0.30. A beam with an intensity profile 1212 as a minimum numerical aperture equal to 0.00, i.e., it is equivalent to the Gaussian beam that fully illuminates a circular aperture.

[0085] Thus, as can be seen from a comparison of the plot FIG. 12A and FIG. 12B, a trade-off exists between minimizing the deleterious effects of the side lobes of the beam and maximizing the axial length of the field of view of the beam. Therefore, by selecting an annulus having a thickness that achieves a length of the field of view that is just sufficient to cover a region of interest in a specimen, but that is not substantially longer than the region of interest, the deleterious effects of the side lobes can be minimized. Therefore, the system 500 shown in FIG. 5, can include a plurality of different apodization masks 506 in which the thickness of the open annular region varies, and a particular one of the apodization masks 506 can be selected to image a region of the specimen 514, where the selected mask is chosen such that the length of the field of view of beam just covers the region of interest. When referring to FIG. 4, the different apodization masks can have open regions with different widths, Δd.

[0086] Thus, a comparison of the plots in FIG. 12A and FIG. 12B shows the profiles of the beam changing from a profile that best approximates that of a lowest order (J₀) Bessel function (plot 1202) to a Gaussian profile (1212). This comparison indicates that the deleterious effect of the side lobes can be reduced by using a beam having a profile that is not substantially similar to that of a Bessel function, at the expense of having a beam with a shorter axial length. This means that it can be advantageous to select a beam profile having a minimum length necessary to create the desired image, so that the effect of the side lobes of the beam, which create background haze and photobleaching, can be minimized. Thus, the beam that may be selected may not have a profile that approximates that of a Bessel function, but the beam also may not have a profile of a Gaussian beam, because the annular mask 506 blocks the portion of the incoming light 504 on the axis of the excitation objective 510 such that the k_z=0 of the beam 516 are removed. In particular, in one implementation, the selected beam can have a ratio of a Rayleigh length, z_R to a minimum beam waist, w_o, of more than 2πw_o/λ and less than 100πw_o/λ. In another implementation, the selected beam can have a non-zero ratio of a minimum numerical aperture to a maximum numerical aperture of less than 0.95. In another implementation, the selected beam can have a non-zero ratio of a minimum numerical aperture to a maximum numerical aperture of less than 0.9. In another implementation, the selected beam can have a ratio of a minimum numerical aperture to a maximum numerical aperture of less than 0.95 and greater than 0.80. In another implementation, the selected beam can have a non-zero ratio of a minimum numerical aperture to a maximum numerical aperture of less than 0.9. In another implementation, the selected beam can have a ratio of a minimum numerical aperture to a maximum numerical aperture of less than 0.95 and greater than 0.80. In another implementation, the selected beam can have a ratio of energy in a first side lobe of the beam to energy in the central lobe of the beam of less than 0.5.

[0087] The length of the beam 516 that is necessary to image a specimen can be reduced by tilting a cover slip that supports the specimen with respect to the direction of the incoming beam 516. For example, if a specimen that resides on a cover slip is 5 μm thick in the direction normal to the cover slip and has lateral dimensions of 50 μm×50 μm then, if the cover slip lies in the Z=0 plane, the beam 516 would have to be 50 μm long to span the specimen. However, by tilting the plane of the cover slip at a 45° angle to the direction of the incoming beam 516, then the beam would only need to be 50 μm/√2 long to span the sample. Thus, by placing a thin specimen on a cover slip and tilting the cover slip with respect to the direction of the incoming beam, a shorter length beam can be used, which has the advantage of reducing the effect of background haze and photobleaching due to side lobes of the beam. To image the specimen on a tilted cover slip, the beam 516 can be scanned in the X direction by tilting the galvanometer-type mirror 902, and can be scanned in the Z direction either by introducing a third galvanometer (not shown) and a third pair of relay lenses (not shown) into the system 900 shown in FIG. 9A to scan the beam 516 in the Z direction or by translating the Z position of the specimen, e.g., via a piezoelectric transducer (not shown and FIG. 9A) coupled to the cover slide that supports the specimen. This mode of operation in which a specimen on a cover slip is imaged when the cover slip is tilted (e.g., at an angle between 10 and 80 degrees) with respect to the direction of the incoming illumination beam can be used to image thin (e.g., less than 10 μm thick) specimens, such as individual cells that are mounted or cultured on to the cover slip.

[0088] Another approach to isolate the central peak fluorescence from the fluorescence generated in the side lobes of the excitation beam is to exclude the latter via confocal filtering with a virtual slit. When the detector includes a plurality of individual detector elements, only those elements of the detector which image the portion of the sample that is illuminated by the central lobe of the illumination beam can be activated to record information that is used to generate an image, while the individual detector elements upon which image the portion of the sample that is illuminated by side lobes of the illumination beam can remain unactivated, such that they do not record information that is used to generate an image.

[0089] For example, FIG. 13A is a schematic diagram of a surface of a detector having a two-dimensional array of individual detector elements in the XY plane. When the center of the central lobe of the excitation beam is located at X=0 and side lobes are located at X>0 and X<0, then the detector elements 1302 onto which fluorescence or detection light is focused from the X=0 position within the specimen at the focal plane of the detection objective 915 (or detector elements corresponding to the smallest absolute value of X for a particular Y position) can be activated to record information, while neighboring detector elements corresponding to higher absolute values of X for the particular Y position can be un-activated such that they do not record information that is used to generate an image. As shown in FIG. 13A, detector elements 1302 located on the detector surface at positions that correspond most closely with fluorescence light from X=0 positions within the specimen can be activated to record information, while neighboring detector elements 1304, 1306 are unactivated, so they do not record fluorescence light from positions within the sample that are not illuminated by the central portion of the excitation beam.

[0090] FIG. 13B is a schematic diagram of “combs” of multiple Bessel-like excitation beams that can be created in a given Z plane. A comb of beams can be created by inserting a diffractive optical element (DOE, not shown) in the beam path between the light source and the galvanometer-type mirrors 902, 905, where the DOE diffracts a plurality of beams at different angles from the DOE, which end up being parallel to and spatially shifted from each other within the specimen. In the specimen at the focal plane of the detection objective, the spacing in the X direction between different beams of the comb is greater than the width of the fluorescence band generated by the side lobes of the beams. This allows information to be recorded simultaneously from rows of individual detector elements corresponding to the centers of the different beams of the comb, without the side lobes of neighboring beams interfering with the recorded signal for a particular beam.

[0091] For example, as shown in FIG. 13B, a comb of beams that illuminate a plane of a specimen 1308 can include the beams A1, B1, C1, D1, and E1, where the beams are separated by distances great enough so that side lobes of one beam in the comb do not overlap with a central portion of a neighboring beam. In this manner, multiple “stripes” of an image can be simultaneously recorded. This process can be repeated, with additional images collected as the comb of Bessel-like illumination beams is translated in discrete steps having a width that corresponds to the spacing in the X direction between individual detector elements until all “stripes” of the final image have been recorded. For example, the beams can be moved to new positions of A2, B2, C2, D2, and E2, where the spacing between the positions A1 and A2, the spacing between positions B1 and B2, etc. corresponds to the spacing between neighboring individual detector elements in the detector. Thus, fluorescence light from the beam position C1 could be detected at a detector element 1302, while fluorescence light from the beam position C2 can be detected at individual detector elements 1304. The image is then digitally constructed from the information in all of the different stripes of the image. An acousto-optical tunable filter (AOTF) 918 can be used to block all excitation light from reaching the specimen between steps.

[0092] Another technique that can be used to reduce the influence of the side lobes and to reduce the Z-axis size of the field of view from which detection light is received is structured illumination (SI) based optical sectioning. In a widefield microscopy implementation of SI, a periodic excitation pattern can be projected through an epi-illumination objective to the focal plane of the objective, and three images of a sample, I_n (n=1,2,3), can be acquired as the pattern is translated in steps of ⅓ of the period of the pattern. Since the observable amplitude of the pattern decreases as it becomes increasingly out of focus (i.e., in a direction perpendicular to the focal plane), combining the images according to:

$\mathrm{Overall}\mathrm{Resolution}=\sqrt{\mathrm{localization}{\mathrm{precision}}^2+\mathrm{Nyqusit}{\mathrm{Resolution}}^2}$

with N=3 removes the weakly modulated out-of-focus component and retains the strongly modulated information near the focal plane. In equation (1), I is an intensity at a point in the image, and n is an index value indicating an image from which I_n is taken. Equation (1) is but one example of a linear combination of the individual images that will remove the weakly modulated out-of-focus component and retain the strongly modulated information near the focal plane.

[0093] To use SI using a Bessel-like beam with a wavelength, λ, that illuminates a thin plane of a specimen and where light is emitted in a direction perpendicular to (or in a direction with a component perpendicular to the illumination plane), the beam may not be swept continuously, but rather can be moved in discrete steps to create a pattern of illumination light from which an image I_n can be generated. When the stepping period is larger than or approximately equal to the minimum period of λ/2NA_Bessel^max required to produce a resolvable grating, but smaller than or approximately equal to λ/NA_Bessel^max, the imposed pattern of illumination light contains a single harmonic, as required for the three-image, three-phase SI algorithm.

[0094] Thus, referring to FIG. 9A, the Bessel-like beam 913 can be moved across the X direction in discrete steps having a period greater than or approximately equal to λ/2NA_Bessel^max and less than or approximately equal to λ/NA_Bessel^max by controlling the position of the galvanometer-type mirror 902, and detection light can be received and signals corresponding to the detected light can be recorded by the detector 917 when the beam 913 is in each of the positions. While the galvanometer-type mirror is being moved from one position to the next position, the illumination light can be blocked from reaching the sample by the AOTF. In this manner, an image I₁ can be generated from the detected light that is received when the illumination beam 913 is at each of its different positions. Then, additional images, I₂ . . . I_N, can be created by again stepping the beam 913 across the specimen in the X direction to create a pattern of illumination light, but with the patterns spatially shifted from the position of the first pattern by (i−1)/N of the period of the pattern, for i=2 to N. A final image of the specimen then can be constructed from the recorded signals through the use of equation (1).

[0095] FIG. 14A shows theoretical and experimental structured illumination patterns that can be created with a 488 nm light Bessel-like beam having a maximum numerical aperture of 0.60 and the minimum numerical aperture of 0.58, that is moved across the X direction in discrete steps. The leftmost column of figures shows theoretical patterns of the point spread functions of the excitation light produced by stepping the beam across the X direction in discrete steps. The middle column shows experimentally-measured patterns, and the third column shows one-dimensional intensity patterns for the Z=0 plane (top figure) and the X=0 (bottom figure) plane, respectively, in each of the three rows of FIG. 14A. In the first row of FIG. 14A, the period the pattern (i.e., the spacing between successive positions of the center of the Bessel-like beam as the beam is stepped in the X direction) is 0.45 μm. In the second row, the period of the pattern is 0.60 μm. In the third row the period of the pattern is 0.80 μm. FIG. 14B shows theoretical and experimental modulation transfer functions (MTFs) in reciprocal space, which correspond to the point spread functions shown in the two left-most columns of FIG. 14A. All of the MTFs are normalized to the maximum frequency, k_max=2NA_exc^max/λ set by Abbe's Law, with NA_exc^max=0.8 for the excitation objective.

[0096] As described above, rather than stepping a single beam across the X direction, a comb of multiple beams, which can be spaced by more than the width of the fringes of the beams in the comb, can be used to illuminate the specimen simultaneously, and then the comb of beams can be stepped in the X direction using the step size described above, so that different stripes of the specimen can be imaged in parallel and then an image of the specimen can be constructed from the multiple stripes.

[0097] The excellent optical sectioning of the single harmonic SI mode results from the removal of the k_x=0 band in the excitation modulation transfer function (MTF) under application of Eq. (1). However, due to the energy in the Bessel side lobes, considerably more spectral energy exists in this band than in the two side bands, so that its removal proves wasteful of the photon budget and reduces the SNR of the final images substantially. Somewhat more energy can be transferred to the side bands using single harmonic excitation having a period far beyond the λ/2NA_detect^max Abbe limit, but at the expense of proportionally poorer optical sectioning capability.

[0098] An alternative that can better retain both signal and axial resolution is to create a multi-harmonic excitation pattern by stepping the beam at a fundamental period larger than λ/NA_Bessel^max, as seen in FIG. 15A, which shows theoretical and experimental higher-order harmonic structured illumination patterns that can be created with Bessel-like beams having a maximum numerical aperture of 0.60 and the minimum vertical aperture of 0.58, which are created with 488 nm light. To create a single SI image with a pattern having H harmonics, Eq. (1) is again used, except with N H+2 images, each with the pattern phase shifted by 2π/N relative to its neighbors.

[0099] FIG. 15B shows theoretical and experimental modulation transfer functions (MTFs) in reciprocal space, which correspond to the point spread functions shown in the two left-most columns of FIG. 15A. As shown in FIG. 15B, with increasing H, more side bands are generated in the MTF that contain a greater combined fraction of the total spectral energy relative to the k_x=0 band, thus yielding higher signal-to-noise (SNR) images. Due to the greater weighting of these sidebands to lower k_z, axial resolution (i.e., along the axis of the detection objective 915) of this multi-harmonic SI mode is slightly less (0.29 μm FWHM for N=9 phases) than in the single harmonic case, yet images of fixed and living cells still exhibit isotropic 3D resolution, albeit at the cost of more data frames required per image plane, and thus lower speed.

[0100] In addition to this speed penalty, both single-harmonic and multi-harmonic SI modes still generate some excitation beyond the focal plane, and are thus not optimally efficient in their use of the photon budget. Both these issues can be addressed using two-photon excitation (TPE), which suppresses the Bessel side lobes sufficiently such that a thin light sheet can be obtained even with a continuously swept beam. As a result, high axial resolution and minimal out-of-focus excitation can be achieved in fixed and living cells with only a single image per plane. Some additional improvement is also possible with TPE-SI, but the faster TPE sheet mode can be preferred for live cell imaging. The benefits of TPE are not limited to structured illumination excitation of the specimen, but can be beneficial during other modes of Bessel-like beam plane illumination of the specimen to reduce out of focus excitation and photo damage by the illumination beam. Other forms of non-linear excitation with a Bessel like beam, such as coherent anti-Stokes Raman scattering (CARS), can also reap similar benefits.

[0101] Thus, the improved confinement of the excitation light to the vicinity of the focal plane of the detection objective made possible by Bessel-like beams and structured plane illumination leads to improved resolution in the axial direction (i.e., in the direction along the axis of the detection objective) and reduced photobleaching and phototoxicity, thereby enabling extended observations of living cells with isotropic resolution at high volumetric frame rates.

[0102] For sufficiently bright samples, the pixel rate of EMCCD cameras can become a limiting factor. To achieve even higher imaging speeds in such cases, a scientific CMOS camera (125 MHz, Hamamatsu Orca Flash 2.8) can be used. To exploit the full speed of the camera, a third galvanometer-type mirror that can be tilted can be placed at a plane conjugate to the rear pupil of the detection objective and used to tile several image planes across the width of the detector, which were then are read out in parallel.

[0103] FIG. 16 shows a system 1600 with a mirror placed at a plane that is conjugate to the detection objective between the detection objective and the detector. In the system 1600, detection light collected by detection objective 1602 can be focused by a tube lens 1604 to form an image at the plane of an adjustable slit 1606. The image cropped by the adjustable slit 1606 is reimaged by relay lenses 1608 onto a high-speed detection camera 1610. A galvanometer-type mirror 1612 is placed at the plane between the relay lenses 1608 that is conjugate to the back focal plane of the detection objective 1612. By changing the angle of galvanometer-type mirror, multiple images can be exposed across the surface of the detection camera 1610 and then read out in parallel to exploit the full speed of the detection camera 1610.

[0104] Three-dimensional live cell imaging can be performed with Bessel-like beams with the use of fluorescent proteins to highlight selected portions of a specimen. The spectral diversity of fluorescent proteins (FPs) permits investigation of the dynamic interactions between multiple proteins in the same living cell. For example, after transfection with mEmerald/MAP4 and tdTomato/H2B, microtubules in a pair of U2OS cells surrounding their respective nuclei, were imaged in the linear, nine-phase multi-harmonic SI mode. Nevertheless, although many vectors are available for linear imaging, the need for N frames of different phase per image plane can limit the use of SI with Bessel-like beams to processes that evolve on a scale that matches the time required to collect frames at the desired spatial resolution. Of course, this limitation does not apply for fixed cells, where the linear SI mode is preferred, due to its superior axial resolution and the availability of a wider array of fluorescent dyes as well as FPs for protein specific labeling. For example, three-color isotropic 3D imaging of the actin cytoskeleton of an LLC-PK1 cell stained with Alexa Fluor 568 phalloidin, the nuclear envelope tagged with mEmerald/lamin B1, and nuclear histones tagged with mNeptune/H2B was performed.

[0105] For imaging multiple proteins exhibiting faster dynamics, the TPE sheet mode can be used. However, this presents its own challenges: orange/red FPs such as tdTomato and mCherry do not have the same TPE brightness and photostability of green FPs such as EGFP or mEmerald and require a second expensive ultrafast light source, since the time required to retune and realign a single source is prohibitive for live cell imaging. Fortunately, the 3D isotropic resolution of the Bessel TPE sheet mode permits multiple proteins tagged with the same FP to be imaged simultaneously, as long as they are known a priori to be spatially segregated.

[0106] As described herein, Bessel beam plane illumination microscopy techniques allows for 3D isotropic high resolution, high imaging speeds, and the ability, in TPE mode, to acquire hundreds of 3D data volumes from single living cells encompassing tens of thousands of image frames. In addition, substantially greater light collection making still better use of the photon budget can be obtained by using a detection objective with a numerical aperture of 1.0 or greater. Even though mechanical constraints of using such a high NA detection objective force the use of an excitation objective with a numerical aperture of less than 0.8, thus lead to a somewhat anisotropic point spread function (PSF), the volumetric resolution remains similar, since the slight loss of axial resolution is offset by the corresponding transverse gain.

[0107] As noted above, SI using the algorithm in Eq. (1) is also photon inefficient, as it achieves high axial resolution by removing substantial spectral energy that resides in the k_x=0 band of the MTF. In some embodiments, the algorithms of 3D superresolution SI can be used, which assign the sample spatial frequencies down-modulated by all bands of the excitation to their appropriate positions in an expanded frequency space. By doing so, shorter exposure times and fewer phases are needed to record images of acceptable SNR, making linear Bessel SI a more viable option for high speed multicolor imaging. In addition, resolution can be extended to the sum of the excitation and detection MTF supports in each direction—an argument in favor of using three mutually orthogonal objectives. Indeed, the marriage of Bessel beam plane illumination and 3D superresolution SI permits the latter to be applied to thicker, more densely fluorescent specimens than the conventional widefield approach, while using the photon budget more efficiently.

[0108] Superresolution SI can be performed by extending the structured illumination techniques described above with respect to FIG. 14 and FIG. 15. By illuminating the sample with a structured illumination pattern, normally inaccessible high-resolution information in an image of a sample can be made accessible in the form of Moiré fringes. A series of such images can be processed to extract this high-frequency information and to generate reconstruction of the image with improved resolution compared to the diffraction limited resolution.

[0109] The concept of super resolution SI exploits the fact that when two patterns are superimposed multiplicatively a beat pattern will appear in the product of the two images, as seen in FIG. 17A. In the case of Bessel-like beam plane illumination microscopy, one of the patterns can be the unknown sample structure, for example, the unknown spatial distribution of regions of the sample that receive illumination light and that emit signal light—and the other pattern can be the purposely structured pattern of excitation light that is written in the form of parallel Bessel-like beams. Because the amount of signal light emitted from a point in the sample is proportional to the product of the local excitation light intensity and the relevant structure of the sample, the observed signal light image that is detected by the detector will show the beat pattern of the overlap of the two underlying patterns. Because the beat pattern can be coarser than those of the underlying patterns, and because the illumination pattern of the Bessel-like beams is known, the information in the beat pattern can be used to determine the normally unresolvable high-resolution information about the sample.

[0110] The patterns shown in FIG. 17A can be Fourier transformed into reciprocal space. For example, the Fourier transform of the structure of a sample that is imaged by an a convention widefield optical system is constrained by the Abbe resolution limit would be represented by a circle having a radius of 2NA/λ, as shown in FIG. 17B, where the low-resolution components of the sample are close to the origin, and the high-resolution components are close to the edge of the circle. The Fourier transform of a 2D illumination pattern that consists of a sinusoidal variation in the illumination light in one dimension and having a period equal to the diffraction limit of the optical system has three non-zero points that lie on the circle shown in FIG. 17C. One point resides at the origin and the other two points are offset from the origin in a direction defined by the orientation of the illumination pattern by distances proportional to the inverse of the spatial period of the pattern. When the specimen is illuminated by structured illumination, the resulting beat pattern between the specimen structure and the illumination structure represents information that has changed position in reciprocal space, such that the observable region of the sample in physical space then contains new high-frequency information represented by the two regions and FIG. 17D that are offset from the origin. For example, the regions of the offset circles in FIG. 17 D that fall outside the central circle represent new information that is not accessible with a conventional widefield technique. When a sequence of such images is obtained using structured excitation radiation that is oriented in different directions, multiple circles that lie outside the central circle are produced, as shown in FIG. 17E. From this plurality of images, information can be recovered from an area that can be twice the size of the normally observable region, to increase the lateral resolution by up to a factor of two is compared with widefield techniques.

[0111] In an implementation using a structured illumination pattern of Bessel-like beams, as explained above with respect to FIG. 14 and FIG. 15, N images can be recorded with the spatial phase of the illumination pattern between each image shifted by A/N in the X direction, where A is the spatial period of the structured illumination pattern and N is the number of harmonics in reciprocal space. Then, a Fourier transform can be performed on each of the N images, and the reciprocal space images can moved to their true positions in reciprocal space, combined through a weighted-average in reciprocal space, and then the weight-averaged reciprocal space image can be re-transformed to real space to provide an image of the sample. In this manner, a superresolution image of the sample can be obtained, where the resolution of the image in both the X and Z directions can be enhanced over the Abbe diffraction limited resolution. The resolution enhancement in the X direction can be up to a factor of two when the NA of the structured excitation and the NA of the detection are the same. However, the excitation lens NA is usually lower than that of the detection lens, so the extension beyond the Abbe limit is usually less than a factor of two but more than a factor of one. In the Z direction, the resolution improvement can be better than a factor of two, since the transverse Z resolution of the excitation can exceed the transverse Z resolution of the detection.

[0112] In another implementation, more than one excitation objective can be used to provide a structured illumination pattern to the sample, where the different excitation objectives can be oriented in different directions, so that super resolution of the sample can be obtained in the directions transverse to the Bessel-like beams of each of the orientation patterns. For example, a first excitation objective can be oriented with its axis along the Y direction (as described above) and can illuminate the sample with an illumination pattern of Bessel-like beams that provides a superresolution image of the sample in the X and Z directions, and a second excitation objective can be oriented with its axis along the X direction and can illuminate the sample with an illumination pattern of Bessel-like beams that provides a superresolution image of the sample in the Y and Z directions. The superresolution information that can be derived from illumination patterns from the different excitation objectives can be combined to yield extended resolution in all three directions.

[0113] In another implementation, highly inclined, objective-coupled sheet illumination has been used to image single molecules in thicker regions of the cell where autofluorescence and out-of-focus excitation would be otherwise prohibitive under widefield illumination. With the thinner light sheets possible with thin light sheet plane illumination, only in-focus molecules would be excited, while out-of-focus ones would not be prematurely bleached. As such, it would be well suited to live cell 3D particle tracking and fixed cell photoactivated localization microscopy.

[0114] At the other extreme, the TPE sheet mode may be equally well suited to the imaging of large, multicellular specimens, since it combines the self-reconstructing property of Bessel beams with the improved depth penetration in scattering media characteristic of TPE. In addition to large scale 3D anatomical mapping with isotropic resolution, at high frame rates it might be fruitfully applied to the in vivo imaging of activity in populations of neurons. When the sample is excited with two-photon excitation radiation, additional spatial frequencies are introduced to images generated from detected light that is emitted from the sample, and the additional spatial frequencies can provide additional information that may be exploited to enhance the resolution of a final image of the sample generated through the super resolution structured illumination techniques described herein. The infrared excitation light used in TPE can penetrate tissue with reduced scattering and aberration, and the out-of-focus emission from the side lobes of the excitation beam can be suppressed. Similarly, the suppression of the side lobes confines the TPE excitation radiation more closely to the Z=0 plane permitting substantial axial resolution improvement when applied to SR-SIM.

[0115] FIG. 18A is a schematic diagram of a system 1800 for generating and providing an array of Bessel-like excitation beams to a sample, similar to the comb of beams show in FIG. 13B, and for imaging the light emitted from the sample due to interaction between the Bessel-like beams and the sample.

[0116] As shown in FIG. 18A, a light source 1802 (e.g., a laser) can produce coherent, collimated light such as a beam having a Gaussian intensity profile, which can be reflected from first galvanometer-type mirror 1804. The mirror 1804 can be controlled by a fast motor 1806 that is used to rotate the mirror and steer the beam in the X direction. After the beam is reflected from the mirror 1804, it is imaged by relay lens pair 1808 and 1810 onto a second galvanometer-type mirror 1812 positioned at a point optically conjugate to the first galvanometer-type mirror 1804. The mirror 1812 can be controlled by a fast motor 1814 that is used to rotate the mirror and steer the beam in the Z direction.

[0117] A second lens pair 1816 and 1818 then can relay the light to a diffractive optical element (DOE) 1824 located just in front of an annular apodization mask (AM) 1822 that is conjugate with the second galvanometer-type mirror 1812. The DOE 1820 can be, for example, a holographic diffractive optical element, that creates, in the far field from the DOE, a fan of Gaussian beams. In some implementations, the DOE can create a fan of seven beams. The apodization mask 1822, located just after the DOE 1820, can be used in combination with the DOE to generate an array of Bessel-like beams in the sample 1840.

[0118] The annular light beams transmitted through the AM 1822 are relayed by a third lens pair 1826 and 1828 onto a conjugate plane co-incident with the back focal plane of excitation objective 1830. Finally, the annular light beams are focused by the objective 1830 to form a fan of Bessel-like beam s that are used to provide excitation light to the sample 1840. The sample 1840 can be placed in an enclosed sample chamber 1832 that can be filled with aqueous media and that can be temperature controlled. Signal light emitted from the sample can be collimated by a detection objective 1834 and focused by a tube lens 1836 onto a position sensitive detector 1838. The signal light emitted from the sample can be generated through a non-linear signal generation process. For example, in one implementation, the signal light may be generated through a two-photon process, such that the signal light has a wavelength that is one half the wavelength of the excitation light of the Bessel-like beams.

[0119] FIGS. 18B and 18C, are example diagrams showing an array of substantially parallel Bessel-like beams produced by the system 1800. FIG. 18B shows the array of beams in the X-Y plane, and FIG. 18C shows the array of beams in the X-Z plane, although FIG. 18C shows only five of the seven Bessel-like beams. In one implementation, a diffractive optical element that produces seven beams in combination with the other beam-forming optics of system 1800, including the apodization mask 1822 and the excitation objective 1830, can create the array of seven Bessel-like beams shown in FIGS. 18B and 18C. As shown in FIGS. 18B and 18C, the beams, for particular parameters and configurations of the beam-forming optics of system 1800, including the dimensions of the apodization mask, the numerical aperture of the excitation objective 1830, etc. the Bessel-like beams that are produced in the sample can extend over a length of approximately 10 μm, and can have central lobes with diameters on the order of 1 μm. FIG. 18D is a schematic figure showing a relative intensity plots of five of the seven Bessel-like beams along the X-axis at the Y=0, Z=0 plane. As shown in FIG. 18D, in this implementation, the intensity profiles of neighboring Bessel-like beams do not substantially overlap. Nevertheless, use of the array of N non-overlapping beams spreads the excitation energy over N beams instead of concentrating the energy in just one beam, and, therefore, the sample is subject to less damage. In addition an array having a plurality of beams can be stepped across the sample to create an incoherent structured illumination pattern over a given field of view faster than one beam can be stepped.

[0120] The rotational axis of galvanometer mirror 1804 can be positioned such that tilting this galvanometer-type mirror 1804 causes the array of Bessel-like beams to sweep across the focal plane of detection objective 1834 (i.e., in the X direction), whose axis is orthogonal to (or whose axis has an orthogonal component to) the axis of the excitation objective 1830. Thus, through control of the galvanometer-type mirror 1804, the array of Bessel-like beams can be swept in the X direction to produce a thin sheet of light in a plane.

[0121] The signal light emitted from the sample 1840 can be directed by detection optics, including the detection objective 1834, to a detector 1838. The galvanometers-type mirrors 1804, 1812 can provide sweep rates of up to about 2 kHz, and with resonant galvanometer-type mirrors (e.g., Electro-Optical Products Corp, model SC-30) sweep rates can exceed 30 kHz. Extremely high frame rate imaging is then possible when the system is used in conjunction with a high frame rate detection camera.

[0122] The rotational axis of the galvanometer mirror 1812 can be positioned such that tilting of this mirror causes the array of Bessel-like beams to translate along the Z axis of detection objective 1834. By doing so, different planes within a specimen can be accessed by the Bessel beam, and a three dimensional (3D) image of the specimen can be constructed, with much higher axial resolution than in conventional light sheet microscopy, due to the much narrower sheet of excitation afforded by array of Bessel-like excitation. In order to image each plane in focus, either detection objective 1834 must be moved synchronously with the motion of the array of Bessel-like beams imparted by the tilt of galvanometer-type mirror 1812 (such as with a piezoelectric transducer), or else the effective plane of focus of the detection objective 1834 must be altered, such as by using a second objective to create a perfect image of the sample. In another implementation, the excitation plane and the detection plane can remain fixed and the sample can be moved through the planes, for example, by using a piezoelectric transducer to move the sample through the beam to cover different z planes. For relatively flat samples, this allows the use of a shorter Bessel-like beams in the Y-direction with less energy in the side-lobes.

[0123] The plurality of Bessel-like beams can lie in a plane within the sample and can be equally spaced from neighboring beams, such that the plurality of beams form a pattern in the plane having a spatial period, A. The array of beams can be scanned in a direction perpendicular to their propagation direction (e.g., in the X direction). In some implementations, the array of beams can be scanned in a series of discrete steps. For example, the array of beams can be scanned from its original position in N−1 discrete steps, where N is an integer, and the steps can have a length of (N−1)·Λ/N. Images of the sample can be recorded based on light emitted from the sample when the array of Bessel-like beams is in each of the N different positions within the sample (i.e., in the original position and in the N−1 scanned positions). Then, a final image of the sample can be generated through a linear combination of the N individual images of the sample. For example, the linear combination of the different images can be created according to

$\begin{array}{cc}{I}_{\mathrm{final}}=\sum _{n=1}^NI_n\exp \left(2\pi n/N\right)& \left(1\right)\end{array}$

where I_final is an intensity of the final image at a particular position within the sample, n is an index variable corresponding to the different individual images that are generated, and In is an intensity of the particular position within the sample in the nth individual image.

[0124] In some implementations, the array of the Bessel-like beams can be spatially dithered (i.e., rapidly changed in a periodic manner) at a dither frequency back and forth in the plane of the array of beams. For example, the galvanometer-type mirror 1804 can be tilted back and forth to dither the spatial position of the array of Bessel-like beams. The array of Bessel-like beams can be spatially dithered over a distance greater than or approximately equal to the spatial period, A, of the pattern of the array of Bessel-like beams. While dithering the array, the Bessel-like beams can be moved in the plane at the array (e.g., along the X axis) at a substantially constant rate, so that the time-averaged intensity of light in the plane of the array is substantially constant. When the inverse of the dither frequency is greater than the integration time of the detector 1838, the excitation light provided by the array of Bessel-like beams in the sample can appear to the detector as a uniform sheet of excitation light.

[0125] The system in FIG. 18A is typically quite wasteful of the energy in light beam 1801, because most of this light is blocked by apodization mask 1808. If greater efficiency is desired, a diffractive optical element such as a binary phase mask or spatial light modulator and a collimating lens can be used to create an approximately annular light beam prior to more exact definition of this beam and removal of higher diffractive orders by the apodization mask 1808.

[0126] The different, substantially parallel Bessel-like beams that are produced from the light of the light source and the beam-forming optics shown in FIG. 18A, can be created from a single source of coherent light, and the beam-forming optics can be held in stable positions, such that fixed phase relationships exist between the different substantially parallel Bessel-like beams in the sample. In some implementations, for example, in the implementation shown in FIGS. 18B, 18C, and 18D, the different Bessel-like beams can be spaced apart from the other with the spacing that is great enough so that the light from neighboring Bessel beams does not interact substantially.

Structured Illumination Microscopy with an Array of Bessel-Like Beams

[0127] Another technique to reduce the influence of the side lobes and to improve the Z-axis resolution of images obtained of a sample is to employ a plane of structured illumination, for example, a 2D optical lattice. Optical lattices are periodic interference patterns in two or three dimensions created by the coherent superposition of a finite number of plane waves travelling in certain well-defined direction. A plane of structured illumination can be created from, for example, a coherent array of Bessel-like beams that are provided simultaneously to the sample, such that interference between the beams of the coherent array improves the Z-axis confinement of the plane of structured illumination that is used to provide excitation radiation to the sample. One way to imagine the creation of such a structured illumination plane is to think of the plane being created by different beams that are spaced apart from their neighboring beams by distances small enough for neighboring beams to overlap and interfere with each other. For example, in some implementations, neighboring Bessel-like beams can be spaced by distances that are less than or comparable to a diameter of a first side lobe of the Bessel-like beams. Interference between the beams then creates a structured light sheet (e.g., an optical lattice) of high modulation depth within the desired Z=0 plane, improving the performance in optically sectioned or superresolution structured plane illumination. In addition, destructive interference between the side lobes outside the Z=0 plane reduces the out-of focus excitation from the side lobes, reducing phototoxicity and decreasing the thickness of the light sheet created by sweeping or dithering the structured light sheet.

[0128] FIG. 19 is a schematic diagram of another system 1900 for producing a structured illumination plane (e.g., an optical lattice) in a sample. As shown in FIG. 19, the light beam from the light source 1902 can be spatially expanded in the X direction by a pair of cylindrical lenses 1904A, 1904B and can be spatially reduced in the Z direction by a pair of cylindrical lenses 1906A, 1906B to produce a beam having an intensity profile that is wide in the X direction and narrow in the Z direction.

[0129] The beam can pass through a beam splitter 1908 and a half-wave plate 1910 and then impinge on a wavefront modulating element (WME) 1912 that independently modulates individual portions of the entire wavefront. The insertion of the half-wave plate 1910 in the beam path can make the WME 1912 operate as a phase modulator of portions of the beam that strike the WME. In some implementations, the WME can include a liquid-crystal phase-only spatial light modulator. In another implementation, the WME can include a ferroelectric binary spatial light modulator. In other implementations, the WME 1912 can include a deformable mirror (e.g., a piston-tip-tilt mirror) or an array of micromirrors. By controlling the WME 1912 (e.g., by control of the individual pixels of a spatial light modulator or individual mirrors within an array of micrometers or control of individual elements of a piston-tip-tilt mirror), the wavefront of the light reflected from the WME 1912, and consequently the wavefront(s) of downstream beam(s) (e.g., beams in the sample 1946), can be controlled. For example, the WME 1912 can be programmed to modulate the wavefront of the incoming light beam such that the outgoing light beam from the WME subsequently defines an array of coherent Bessel-like beams that overlap and interfere with each other to create a plane of structured illumination in the sample 1946. The WME 1912 can be optically conjugated to the sample 1946, so that modulations introduced by the WME can be propagated to the sample.

[0130] The WME 192 can be used to control the relative phases of individual beamlets (or portions of the incoming wavefront) that are reflected from the WME. For example, the WME 1912 can be used to control the relative phases of individual portions of the wavefront that strike the WME 1912 and that then propagate into the sample 1946. In some implementations, this relative phase control of individual portions of the reflected wave front can result in control of relative phases of individual Bessel-like beams in array of beams in the sample 1946.

[0131] In some implementations, the WME 1912 can include a spatial light modulator, and in some implementations the spatial light modulator can be a binary spatial light modulator, in which each pixel of the spatial light modulator can have one of two different states that affect the light modulated by the pixel. In some implementations, the WME 1912 can be used to scan the array of Bessel-like beams within the sample—either within the plane of the array or perpendicular to the plane (e.g. in the Z axis direction).

[0132] An advantage of using a reflective spatial light modulator (SLM) as the WME is that, with a high number of pixels (e.g., 1024×1280 pixels), it can be readily divided into many subregions, and in part because the subregions are truly independent, and not mechanically coupled, as in a deformable mirror.

[0133] After modulation by the WME 1912, the light reflected from the WME can be reflected by the beam splitter 1908 and reflected by mirrors 1914, 1916. Then, the light can be imaged by a lens 1918 onto an apodization mask 1920 that is conjugate to the rear pupil of the excitation objective 1942. After the apodization mask 1920, the light can be reflected off of a mirror 1922, transmitted through relay lenses 1924, 1926, reflected off galvanometer mirror 1928, mirror 1930, transmitted through relay lenses 1932, 1934, reflected off galvanometer mirror 1936, and transmitted through relay lenses 1938, 1940 to the rear pupil plane of excitation objective 1942. Then, the light can be focused by excitation objective 1942 onto the sample 1946 that is housed in chamber 1944.

[0134] Mirror 1928 can operate as a galvanometer-type mirror to translate the structured plane illumination in the X direction within the sample, and the mirror 1928 can be conjugated to the apodization mask 1920 by relay lenses 1924, 1926. Mirror 1936 can operate as a galvanometer-type mirror to translate the structured plane illumination in the Z direction within the sample, and the mirror 1936 can be conjugated to mirror 1928 by relay lenses 1932, 1934. The rear pupil plane of excitation objective 1942 can be conjugated to mirror 1936 by relay lenses 1938 and 1940. The combination of lenses 1918, 1924, 1926, 1932, 1934, 1938, and 1940 as well as excitation objective 1942 then serve to conjugate WME 1912 to an excitation plane within the sample 1946. The sample 1946 can be supported on a translation stage 1947 that can be used to translate the sample in space. In some implementations, the translation stage 1947 can translate the sample 1946 with respect to a beam of radiation that is provided to the sample, while the position of the beam remains fixed.

[0135] Light emitted from the sample 1946 due to the interaction of the excitation light with the sample can be collected by the detection objective 1948 and then focused by lens 1950 onto a detector 1952. Information collected by the detector 1952 can be sent to a computing device 1954, which may include one or more processors and one or more memories. The computing device may process the information from the detector 1952 to create images of the sample 1946 based on the information provided by the detector 1952.

[0136] The WME 1912 can control the wavefront of the light leaving the WME, such that the plurality of Bessel-like beams is created in the sample 1946. Furthermore, the WME 1912 can control the relative phases of the individual Bessel-like beams in the sample. The relative phases of the individual Bessel-like beams can be controlled such that neighboring Bessel-like beams interfere destructively with each other at positions that are out of the plane of the array of Bessel-like beams. For example, the destructive interference can occur within the Z≠0 plane when the array of Bessel-like beams is in the Z=0 plane. For example, the first side lobes of neighboring Bessel-like beams can destructively interfere where they intersect with each other at locations that are not in the plane of the array. For example, the intersection point can occur at a position that is closer to the plane of the array than a diameter of the first side lobe of the Bessel-like beams. Techniques for using a spatial light modulator WME to create structured light sheets within the sample are described in more detail below.

[0137] The system 1900 can operated the microscope in different modes—e.g., a super-resolution structure illumination microscopy (SIM) mode or a high speed dithered mode. In the SIM mode, F images can be recorded at multiple different z planes as the plane of structured illumination (e.g., the lattice light sheet) is stepped in the x direction in F equal fractions of the period of the structured illumination, and images of the fluorescence light from the sample are detected. This data then can be used to reconstruct a 3D image with resolution extending beyond the diffraction limit in x and z. In the dithered mode, we the galvanometer mirror 1928 can be used to oscillate the lattice pattern back and forth in x at an amplitude larger than the lattice period and a speed fast compared to the exposure time of the detector, providing time-averaged uniform illumination across the xy plane. In this mode, only one 2D image needs to be recorded at each z plane, but the resolution remains diffraction limited.

[0138] FIG. 20 is a flowchart of a process 2000 of determining a pattern to apply to a binary spatial light modulator, which will produce a coherent structured light sheet (e.g., an optical lattice) having a relatively low thickness in the Z direction over a sufficient length in the Y direction to image samples of interest. In the process 2000, the complex electric field

E_b(x,z)

of a single Bessel-like beam propagating in the Y direction into the sample is calculated (step 2002). The complex electric field is chosen based on a maximum NA to achieve a desired maximum X-Z spatial frequency and based on a minimum NA to achieve a desired beam length in the Y direction. Then, the complex electric field

E_tot(x,z)

of the structured light sheet that is formed by a coherent sum of a plurality of Bessel-like beams in a linear periodic array of Bessel-like beams can be calculated (step 2004). The total complex electric field of the array of beams can be expressed as:

$I_{\mathrm{final}}=\sum _{n=1}^NI_n\exp \left(2\pi n/N\right).$

where α is the phase difference between adjacent beams in the array, and for T is the spatial period of the array of beams. In some implementations, a can be set equal to 0 or π (i.e., all beams can have the same phase, or beams can have alternating opposite phases). Then, the real scalar field in the desired polarization state can be determined (step 2006), where the real scalar field is given by:

E_tot(x,z)=Re{E_tot(x,z)·e_d}

[0139] Next, the real scalar field can be multiplied by an envelope function ψ(z) that bounds the excitation light to the desired vicinity of the ideal Z=0 illumination plane (step 2008). The product of the real scalar field and the envelope function gives the function for the bound field:

E_bound(x,z)=ψ(z)E_tot(x,z)

In some implementations, the envelope function can be a Gaussian function:

ψ(z)=exp(−z²/a²)

Then, the field values having a magnitude lower than a threshold value, ε, can be set to zero (step 2010). The thresholding step can be expressed mathematically as:

E_thresh(x z)=Θ(|E_bound(x z)|−ε)E_bound(x,z)

where Θ(ζ)=1, for ζ>0 and 0 for ζ<0. Then, individual pixels values of a binary SLM that is used as the WME 1912 can be set to impose a 0 or π phase shift on light that interacts with the SLM (step 2012), according to:

SLM(x_p,z_p)=Θ(E_thresh(x_p,z_p))π,

where the “p” subscript references an individual pixel of the SLM.

[0140] FIGS. 21A-21F show a series of graphical illustrations of the process 2000, when the processes used to generate a thin array of structured excitation radiation that is swept in the X direction to generate a plane of excitation illumination. FIG. 21A illustrates a cross-sectional profile in the X-Z plane of a Bessel like beam propagating in the Y direction. The particular cross section shown in FIG. 21A is for a Bessel-like beam having a maximum numerical aperture of 0.60 and a minimum numerical aperture of 0.54. Higher electric field strengths are shown by whiter regions in FIG. 21A.

[0141] FIG. 21B illustrates the electric field, in the X-Z plane, of a structured light sheet formed by coherent sum of a linear, periodic array of Bessel-like beams that propagate in the Y direction. The individual Bessel-like beams have a maximum numerical aperture of 0.60 and a minimum numerical aperture is 0.54. The wavelength of the light is 488 nm, and the period of the array of beams is 0.90 μm, and the individual beams of the array all have the same phase. Higher electric field strengths are shown by whiter regions in FIG. 21B. The lengths shown on the axes of all of the panels of FIG. 21A-21F are normalized to the wavelength of light in the medium within the sample chamber 1944.

[0142] FIG. 21C illustrates the electric field, in the XZ plane, of the structured light sheet of FIG. 21B after a Gaussian envelope function has been applied to the field of the light sheet to bound the light sheet in the Z direction. Higher electric field strengths are shown by whiter regions. FIG. 21D illustrates the pattern of phase shifts applied to individual pixels of a binary spatial light modulator to generate the field shown in FIG. 21C. Pixels generating a phase shift of π are shown in black, and pixels generating a phase shift of zero are shown in white. FIG. 21E illustrates the cross-sectional point spread function, in the X-Z plane, of the structured plane of excitation radiation that is produced in the sample by the coherent array of Bessel-like beams, which are generated by the pattern on the spatial light modulator shown in FIG. 21D. Higher light intensities are shown by whiter regions. FIG. 21F illustrates the time-averaged excitation beam intensity that is produced in the sample when the structured plane of excitation radiation swept or dithered in the X direction. Higher intensities are shown by whiter regions.

[0143] Changing the period of the array of the coherent beams can affect the overall electric field pattern resulting from the interference of the plurality of beams. In particular, for different periods of the array, the resulting electric field interference pattern can extend relatively more or less in the Z direction. This effect can be exploited to determine parameters of the coherent array that can be useful for generating images of the sample using super resolution structured illumination techniques as well as using a thin sheet of structured illumination that is swept in the X direction.

[0144] FIGS. 22A-22F show a series graphical illustrations of the process 2000, when the plane is used to generate an array of structured excitation radiation that is used to generate images of the sample using super resolution structured illumination techniques. Like FIG. 21A, FIG. 22A illustrates a cross-sectional profile in the X-Z plane of a Bessel like beam propagating in the Y direction. The particular cross section shown in FIG. 22A is identical to that of FIG. 21A and is for a Bessel-like beam having a maximum numerical aperture of 0.60 and a minimum numerical aperture of 0.54. The lengths shown on the axes of all of the panels of FIGS. 22A-22F are normalized to the wavelength of light in the medium within the sample chamber 1944.

[0145] FIG. 22B illustrates the electric field, in the X-Z plane, of a structured light sheet formed by a coherent sum of a linear, periodic array of Bessel-like beams that propagate in the Y direction. The individual Bessel-like beams have a maximum numerical aperture of 0.60 and a minimum numerical aperture is 0.54. The wavelength of the light is 488 nm, and the period of the array of beams is 0.92 μm and the individual beams of the array all have the same phase. Thus, the period of the array illustrated in FIG. 22B is 0.02 μm longer than the period of the array illustrated in FIG. 21B.

[0146] FIG. 22C illustrates the electric field, in the XZ plane, of the structured light sheet of FIG. 22B after a Gaussian envelope function has been applied to the field of the light sheet to bound the light sheet in the Z direction. Because these structured light sheets can be used for super resolution structured illumination microscopy, in which it may be desirable to have the electric field extend further in the Z direction then when using the light sheet in a swept sheet mode, the envelope (or “bounding”) function used in FIG. 22C may be relatively more relaxed than the bounding function used in FIG. 21C.

[0147] FIG. 22D illustrates the pattern of phase shifts applied to individual pixels of a binary spatial light modulator to generate the field shown in FIG. 22C. Pixels generating a phase shift of π are shown in black, and pixels generating a phase shift of zero are shown in white. FIG. 22E illustrates the cross-sectional point spread function, in the X-Z plane, of the structured plane of excitation radiation that is produced in the sample by the coherent array of Bessel-like beams, which are generated by the pattern on the spatial light modulator shown in FIG. 22D. FIG. 22F illustrates the modulation transfer function, which corresponds to the point spread functions shown in FIG. 22E. All of the MTFs are normalized to 4π/λ, where λ is the wavelength of light in the medium within the sample chamber 1944.

[0148] As can be seen from the electric field patterns and point spread function structured illumination plane patterns in FIGS. 21A-21F and 22A-22F, the coherent superposition of a plurality of Bessel-like beams bears little resemblance to the electric field patterns and point spread function patterns of individual Bessel-like beams. As is evident from a comparison of FIGS. 21A-21F and FIGS. 22A-22F, changing the period of the array of beams causes large changes in optical properties of the optical lattices (e.g., the period, symmetry, and degree of bounding in the Z direction of the lattices) that result from interference between the beams of the array. Instead, the coherent superposition of an array of Bessel-like beams, in general, can form a spatially-structured plane of excitation radiation (e.g., an optical lattice) that can be used to excite optical labels within a sample, which then emit light that is detected and used to generate an image of the sample. In some implementations, the spatially-structured plane of excitation radiation can be swept in a direction parallel to the plane to generate a thin sheet of excitation radiation. In some implementations, the spatially-structured plane of excitation radiation can be translated in discrete steps in a direction parallel to the plane and emit light can be detected when the plane is in each of the different positions. Then, the light detected from the sample when the plane is in each of the different positions can be algorithmically combined to generate a super resolution image of the sample.

[0149] FIGS. 23A-23F are a schematic diagram of the intensities of different modes of excitation radiation that can be provided to the sample. FIG. 23A is a cross-section in the X-Z plane of a Bessel-like beam propagating in the Y direction. The particular cross section shown in FIG. 23A is for a Bessel-like beam having a wavelength of 488 nm and having a maximum numerical aperture of 0.60 and a minimum numerical aperture of 0.54. Higher intensities are shown by whiter regions. When the Bessel-like beam of FIG. 23A is swept in the X direction, then the time-averaged intensities in the X-Z plane shown in FIG. 23B results. FIG. 23C is a cross-sectional in the X-Z plane of a superposition of incoherent Bessel-like beams propagating in the Y direction, such as would occur if the single Bessel-like beam in FIG. 23A were moved in discrete steps. The pattern shown in FIG. 23C is for a 488 nm Bessel-like beam having a maximum numerical aperture of 0.60 and a minimum numerical aperture of 0.54, stepped in units of 0.90 μm. When multiple instances of the array of Bessel-like beams of FIG. 23C are moved in small increments in the X direction and the resulting signal integrate don a camera, then the time-averaged intensity in the X-Z plane shown in FIG. 23D results. FIG. 23E is a cross-section in the X-Z plane of a superposition of coherent Bessel-like beams propagating in the Y direction. The pattern shown in FIG. 23E is for an array of 488 nm Bessel-like beams having a maximum numerical aperture of 0.60 and a minimum numerical aperture of 0.54, with individual beams of the array being spaced 0.90 μm from each other. When the array of Bessel-like beams of FIG. 23E is swept or dithered in the X direction, then the time-averaged intensity in the X-Z plane shown in FIG. 23F results. As can be seen by a comparison of FIG. 23B, FIG. 23D, and FIG. 23F, the coherent array of Bessel-like beams can result in a light sheet that is more tightly confined in the Z direction that a light sheet that is produced by sweeping a single Bessel-like beam (FIG. 23B) or a light sheet that is produced by sweeping an incoherent array of Bessel-like beams (FIG. 23D).

[0150] Referring again to the electric field patterns in FIGS. 21B and 22B, and point spread function intensity patterns in FIGS. 21E and 22E, it can be seen that the coherent superposition of a plurality of Bessel-like beams forms a spatially-structured plane of excitation radiation. These patterns can be viewed as optical lattices that are created by interference within the sample between different beamlets of the beam that is modulated by the spatial light modulator 1912 shown in FIG. 19 and then enter the sample 1946 through the excitation objective 1942. Therefore, in some implementations, a pattern can be applied to the WME 1912 that creates an optical lattice within the sample, which can be used to generate a spatially-structured plane of excitation radiation that can be used to generate images of the sample 1946.

[0151] FIG. 24 is a flowchart of a process 2400 of determining a pattern to apply to a binary spatial light modulator, which will produce an optical lattice within the sample, where the optical lattice can be used as a coherent structured light sheet (e.g., an optical lattice) having a relatively low thickness in the Z direction over a sufficient length in the Y direction to image samples of interest. In the process 2400, the complex electric field E_lattice(x, z) of a selected two-dimensional 2D optical lattice can be calculated (step 2402). The selected optical lattice can be, for example, a fundamental lattice, a sparse lattice, a composite lattice, or a maximally symmetric composite lattice, as described in U.S. Pat. No. 7,609,391, entitled “Optical Lattice Microscopy,” issued on Oct. 27, 2009, which is incorporated herein by reference. In some implementations, a maximally symmetric composite lattice can be selected to provide tight confinement of the excitation radiation in the Z direction when generating images of the sample using the swept sheet mode and to provide high spatial frequency components in the XZ plane when generating images of the sample using the super resolution, structured illumination mode. In some implementations, maximally symmetric composite hexagonal and square lattices can be used, because they can provide more wavevectors than lattices with other symmetry.

[0152] Then, the lattice can be rotated about the Y axis to a desired orientation (step 2404). For example, an orientation of the lattice in which lattice wavevectors lie along the X axis facilitates the construction of structured light sheets that are tightly confined in the Z direction. In another example, an orientation of the optical lattice in which a line of lattice intensity maxima lies along the x-axis can be desirable. In another example, an optical lattice having a periodicity and orientation such that adjacent lines of the lattice maximum along the X direction are separated by more than the desired light sheet thickness in the Z direction can be useful when using the lattice to generate images of the sample with the swept sheet mode. However, the lines of lattice maximum along the X direction can be separated by less than the desired light sheet thickness when using the super resolution, structured illumination mode to generate images of the sample.

[0153] After the orientation of the lattice is determined, the real scalar field of the optical lattice can be determined (step 2406), where the real scalar field is given by:

E_lattice(x,z)=Re{E_lattice(x,z)·e_d},

Where e_d is a vector in the direction of the desired polarization of the electric field. Next, the real scalar field of the optical lattice can be multiplied by an envelope function ψ(z) that bounds the excitation light to the desired vicinity of the ideal Z=0 illumination plane (step 2408). The product of the real scalar field and the envelope function gives the function for the bound field:

E_bound(x,z)=ψ(z)E_lattice(x,z).

In some implementations, the envelope function can be a Gaussian function:

ψ(z)=exp(−z²/a²)

Then, the field values having a magnitude lower than a threshold value, ε, can be set to zero (step 2410). The thresholding step can be expressed mathematically as:

E_thresh(x,z)=Θ(|E_bound(x,z)|ε)E_bound(x,z)

where Θ(ζ)=1, for ζ>0 and 0 for ζ<0. Then, individual pixels values of a binary SLM that is used as the WME 1912 can be set to impose a 0 or π phase shift on light that interacts with the SLM (step 2412), according to:

SLM(x_p,z_p)=Θ(E_thresh(x_p,z_p))π.

where the “p” subscript references an individual pixel of the SLM. This pattern imposed on the SLM, which is conjugate to the sample 1946, will create an optical lattice within the sample.

[0154] Optical lattices optimized for the dithered mode can include a maximally symmetric fundamental rectangular lattice. In some implementations, the lattice can have a period along the z-axis that is 1.5× greater than the period along the x-axis, where the x period=2.641×NA_exc×λ_exc/n, where NA_exc and λ_exc are the numerical aperture and free space wavelength, respectively, of the light used to create the ideal lattice, and n is the refractive index of the imaging medium. The ideal lattice can be comprised of four wavevectors. Optical lattices optimized for the dithered mode can include a maximally symmetric fundamental square lattice, rotated to place two of the four wavevectors of the ideal lattice along the x axis, so that these two wavevectors become two vertical bands in the bound lattice, which are then clipped by the annulus of the apodization mask to create four smaller vertical bands in the rear pupil. In some implementations, the lattice can have an x period=4.828×NA_exc×λ_exc/n. Optical lattices optimized for the dithered mode can include a maximally symmetric fundamental hexagonal lattice, rotated to place two of the six wavevectors of the ideal lattice along the z axis. The ideal lattice is comprised of six wavevectors. In some implementations, the lattice can have an x period=4.896×NA_exc×λ_exc/n. Optical lattices optimized for the dithered mode can include a maximally symmetric first order sparse square lattice. In some implementations, the lattice can have an x period=6.952×NA_exc×λ_exc/n. Optical lattices optimized for the dithered mode can include a maximally symmetric first order sparse square lattice, rotated 45° with respect to the lattice describe immediately above. The ideal lattice is comprised of eight wavevectors. In some implementations, the lattice can have an x period=9.485×NA_exc×λ_exc/n. Optical lattices optimized for the dithered mode can include a maximally symmetric first order sparse hexagonal lattice. In some implementations, the lattice can have an x period=20.92×NA_exc×λ_exc/n. The ideal lattice is comprised of twelve wavevectors.

[0155] Lattices optimized for the SIM mode, where the axial modulation depth and spatial frequency have been optimized to produce high resolution in the z direction when used in the structured illumination mode, can include a fundamental hexagonal lattice, comprised of three wavevectors, rotated to place one of the wavevectors on the x axis. The pattern requires three phase-stepped images for SIM reconstruction. Lattices optimized for the SIM mode can include a maximally symmetric fundamental square lattice, but with less axial confinement than the maximally symmetric fundamental square lattice that is used in the dithered mode, for optimization in the SIM mode. Five phase-stepped images are required for SIM reconstruction. Lattices optimized for the SIM mode can include a maximally symmetric fundamental hexagonal lattice but also with reduced axial confinement compared to the same lattice that is used is optimized for the dithered mode. Five or nine phase-stepped images are required for SIM reconstruction, depending on the orientation of the lattice with respect to the x axis. Lattices optimized for the SIM mode can include a maximally symmetric first order sparse square lattice, except with reduced axial confinement compared to the same lattice that is used is optimized for the dithered mode. Seven or nine phase-stepped images are required for SIM reconstruction, depending on the orientation of the lattice with respect to the x axis.

[0156] FIGS. 25A-25E show a series of graphical illustrations of the process 2400, when the process is used to generate an optical lattice of structured excitation radiation that is swept in the X direction to generate a plane of excitation illumination. FIG. 25A illustrates a cross-sectional profile in the X-Z plane of an ideal two-dimensional fundamental hexagonal lattice that is oriented in the Z direction. The optical lattice is formed by the coherent superposition of a plurality of beams that all converge on a cone corresponding to a numerical aperture of 0.51. The profile shows the real electric field strengths in the optical lattice, with higher electric field strengths being shown by whiter regions. The lengths shown on the axes of all of the panels of FIG. 25 are normalized the wavelength of light in the medium within the sample chamber 1944.

[0157] FIG. 25B illustrates the electric field, in the XZ plane, of the optical lattice of FIG. 25A after a Gaussian envelope function has been applied to the optical lattice to bound the lattice in the Z direction. Higher electric field strengths are shown by whiter regions. FIG. 25C illustrates the pattern of phase shifts applied to individual pixels of a binary spatial light modulator to generate the field shown in FIG. 25B. Pixels generating a phase shift of π are shown in black, and pixels generating a phase shift of zero are shown in white. FIG. 25D illustrates the cross-sectional point spread function, in the X-Z plane, of the structured plane of excitation radiation that is produced in the sample by the optical lattice, which is generated by the pattern on the spatial light modulator shown in FIG. 25C, and then filtered by an annular apodization mask that limits the maximum NA of the excitation to 0.55 and the minimum NA of the excitation to 0.44. Higher intensities are shown by whiter regions. FIG. 25E illustrates the excitation beam intensity that is produced in the sample when the bound optical lattice pattern in FIG. 25D is swept or dithered in the X direction. Higher intensities are shown by whiter regions.

[0158] FIGS. 26A-26F illustrate the light patterns at a plurality of locations along the beam path shown in FIG. 19 when the pattern shown in FIG. 25C is used on the SLM 1912. For example, FIG. 26A is identical to FIG. 25C and illustrates the pattern of phase shifts applied to individual pixels of a binary spatial light modulator 1912 to generate the field shown in FIG. 25B. FIG. 26B illustrates the intensity of light that impinges on the apodization mask 1920 downstream from the SLM 1912. FIG. 26C illustrates the transmission function of the apodization mask 1920, and FIG. 26D illustrates the intensity of light immediately after the apodization mask 1920. As shown in FIG. 26D, the pattern of the light that exists just after the apodization mask 1920, which is conjugate to the rear pupil of the excitation objective, is a plurality of six vertical slits located on a surface of a cone, and when this pattern is focused by the excitation objective 1942 to the focal plane within the sample, the optical lattice shown in FIG. 26E (which is identical to the pattern shown in FIG. 25D) results. When this optical lattice is swept or dithered in the X direction, the sheet of excitation radiation shown in FIG. 26F results. The lengths shown on the axes of all of the panels of FIGS. 26A-26F are normalized to the wavelength of light in the medium within the sample chamber 1944.

[0159] FIGS. 27A-27F shows a series of graphical illustrations of the process 2400, when the processes used to generate an optical lattice of structured excitation radiation that is translated in the X direction in discrete steps to generate images of the sample using superresolution, structured illumination techniques. FIG. 27A illustrates a cross-sectional profile in the X-Z plane of a two-dimensional fundamental hexagonal lattice that is oriented in the Z direction. The optical lattice is formed by the coherent superposition of a plurality of beams that all converge on a cone corresponding to a numerical aperture of 0.57. The lengths shown on the axes of all of the panels of FIGS. 27A-27F are normalized to the wavelength of light in the medium within the sample chamber 1944.

[0160] FIG. 27B illustrates the electric field, in the XZ plane, of the optical lattice of FIG. 27A after a Gaussian envelope function has been applied to the optical lattice to bound the lattice in the Z direction. Higher electric field strengths are shown by whiter regions. The envelope function used for FIG. 27B confines the lattice less tightly in the Z direction that the envelope function used for FIG. 25B. FIG. 27C illustrates the pattern of phase shifts applied to individual pixels of a binary spatial light modulator to generate the field shown in FIG. 27B. Pixels generating a phase shift of π are shown in black, and pixels generating a phase shift of zero are shown in white. FIG. 27D illustrates the cross-sectional point spread function, in the X-Z plane, of the structured plane of excitation radiation that is produced in the sample by the optical lattice, which is generated by the pattern on the spatial light modulator shown in FIG. 27C, and then filtered by an annular apodization mask that limits the maximum NA of the excitation to 0.60 and the minimum NA of the excitation to 0.54. Higher intensities are shown by whiter regions. FIG. 27E illustrates the modulation transfer function, in reciprocal space, which corresponds to the intensity pattern shown FIG. 27D. The MTF is normalized to 4π/λ, where λ is the wavelength of the excitation radiation. Higher spectral powers are shown by whiter regions.

[0161] FIGS. 28A-28F illustrates the light patterns at a plurality of locations along the beam path shown in FIG. 19 when the pattern shown in FIG. 27C is used on the SLM 1912. For example, FIG. 28A is identical to FIG. 27C and illustrates the pattern of phase shifts applied to individual pixels of a binary spatial light modulator 1912 to generate the field shown in FIG. 27B. FIG. 28B illustrates the intensity of light that impinges on the apodization mask 1920 downstream from the SLM 1912 when the SLM includes the pattern of FIG. 28A. FIG. 28C illustrates the transmission function of the apodization mask 1920, and FIG. 28D illustrates the intensity of light immediately after the apodization mask 1920. The mask used to produce the transmission function shown in FIG. 28C includes the product of an annular mask and a mask having two slits, which transmits only three of the six beams shown in FIG. 28B. As shown in FIG. 28D, the pattern of the light that exists just after the apodization mask 1920, which is conjugate to the rear pupil of the excitation objective, is a plurality of three vertical slits located on a surface of a cone, and when this pattern is focused by the excitation objective 1942 to the focal plane within the sample, the optical lattice shown in FIG. 28E (which is identical to the pattern shown in FIG. 27D) results. The modulation transfer function for this lattice is shown in FIG. 28F. The lengths shown on the axes of all of the panels of FIG. 28 are normalized the wavelength of light in the medium within the sample chamber 1944.

[0162] Referring again to FIGS. 25A-25E, and, in particular, to FIG. 25B, the envelope functions that are selected to bound the optical lattice to the vicinity of the Z=0 plane of the sample can have an effect on the intensity pattern of the swept light sheet shown in FIG. 25E. For example, when a strong envelope function is selected that tightly binds the optical lattice to the vicinity of the Z=0 plane, then the intensity of the optical lattice may be strongly confined to the line of intensity maxima along the Z=0 plane, but the extent of the individual maxima in the Z direction can be relatively large. On the other hand, when a weak envelope function is selected that only loosely binds the optical lattice to the vicinity of the Z=0 plane, then the optical lattice within the sample may include intensity maxima along the line of the Z=0 plane and also maxima along one or more lines that are displaced from the Z=0 plane. This phenomenon is shown in FIGS. 29A-29H.

[0163] FIGS. 29A-29H are a plurality of graphs illustrating the effect of the Z axis bounding of the optical lattice on the light sheets produced in the sample. FIG. 29A illustrates the intensity of the optical lattice to which a wide, or weak, envelope function is applied. As can be seen in FIG. 29A, intensity maxima exist along the Z=0 plane and also at positive and negative nonzero values of Z. Sweeping or dithering this pattern in the X direction creates a light sheet whose intensity profile along the Z direction is shown in the curve A of FIG. 29B. Curve A shows side lobes peaked at three wavelengths away from the Z=0 plane. Curve B shown in FIG. 29B shows the point spread function of the detection objective 1948, and the curve C in FIG. 29B shows the normalized product of curves A and B, which is the overall point spread function of the optical system in the Z direction. In some implementations, the numerical aperture of the excitation objective and the numerical aperture of the detection objective can be selected such that the maximum intensity of a side lobe of the sheet of excitation illumination occurs at a Z position that corresponds to a minimum in the point spread function of the detection objective. In this manner, the overall point spread function shown in curve C can minimize the effect of the excitation illumination side lobes on images generated from the sample. The lengths shown on the axes of all of the panels of FIG. 29 are normalized the wavelength of light in the medium within the sample chamber 1944.

[0164] FIG. 29G illustrates the intensity of the optical lattice to which a narrow, or strong, envelope function is applied to the ideal optical lattice pattern. As can be seen in FIG. 29G, intensity maxima exist along the Z=0 plane, but there are no lines of intensity maxima along other planes. Sweeping or dithering this pattern in the X direction creates a light sheet whose intensity profile along the Z direction is shown in curve A of FIG. 29H. Curve A shows much smaller side lobes peaked at three wavelength away from the Z=0 plane than in FIG. 29B. Curve B shown in FIG. 29H shows the point spread function of the detection objective 1948, and curve C in FIG. 29H shows the normalized product of curves A and B, which is the overall point spread function of the optical system in the Z direction. As can be seen from a comparison of FIG. 29B and FIG. 29H, the central peak in curve A of FIG. 29B is narrower than the central peak in curve A of FIG. 29H, but the side lobes of FIG. 29B are larger than the side lobes and FIG. 29H. Thus, bound optical lattices having different parameters can be selected to image different samples using different techniques. FIG. 29C and FIG. 29D are similar to FIGS. 29A and 29B, respectively, and to FIGS. 29G and 29H, respectively, except that a medium-wide envelope function is used. FIG. 29E and FIG. 29F are similar to FIGS. 29A and 29B, respectively, and to FIGS. 29G and 29H, respectively, except that a medium-narrow envelope function is used.

Stochastic Excitation of Individually-Localizable Optical Labels with Thin Light Sheets

[0165] The thin light sheets described herein can be used with techniques that involve using stochastic activation and/or excitation of individual emitting labels within a sample to create high-resolution images of the sample. With stochastic activation and/or excitation, individual emitters within the sample can be individually resolved as their emission of signal light is turned on and off, and the thin sheet of activation and/or excitation radiation can limit the amount of signal light that is produced in portions of the sample that are not in the focal plane of the detection objective. As different emitting labels are turned on and off within a focal plane of the detection objective, an image of the sample at that plane can be built up over time. Also, the focal plane of the detection objective can be moved through the sample, and the thin sheet of activation and/or excitation radiation can be moved along with the focal plane, so that multiple planes of the sample can be imaged, which may allow generation of a three-dimensional image of the sample.

[0166] In some implementations, a sample can include a dense plurality of phototransformable or photoswitched optical labels (“PTOLs”), such as, for example, photoactivated or photoswitched fluorescent proteins (“FPs”), that are transformable from an inactive state (in which the labels do not produce significant detectable radiation when excited) to an activated state (in which the labels can emit radiation when excited) by virtue of the interaction of the transformable labels with their environment. With sufficient control over at least one activating environmental parameter, a controllable, sparse subset of the labels can be activated. These activated labels can then be excited into excited states, from which they can emit fluorescence radiation that can be imaged by an optical system. By controlling the activation environment and exciting radiation, the mean volume per activated and excited label that emits radiation can be greater than the diffraction-limited resolution volume (“DLRV”) characteristic of the optical system. By detecting radiation from such a sparse subset of emitting labels, the location of the activated and excited PTOLs can be determined with superresolution accuracy. Then, the activated labels can be deactivated, and another subset of transformable labels, statistically likely to be located at different positions within the sample, can be activated by controlling at least one activating environmental parameter, and fluorescence from the second subset of activated labels can be imaged, and their locations can be determined with superresolution accuracy. This process can be repeated to determine the location of more transformable labels within the sample with superresolution accuracy. The determined locations of all the transformable labels from the different images can be combined to build up a superresolution image of the sample.

[0167] FIG. 30 is a schematic diagram illustrating a PTOLs (e.g., a fluorescent molecule) 3001 stimulated by excitation radiation 3002 from a ground state into an excited state 3003 that emits a portion of the energy of the excited state into a fluorescence radiation photon 3004. The molecule 3001 then reverts to the ground state 3005. This cycle of excitation of the molecule 3001 by radiation 3002 and emission of fluorescence radiation 3004 can be repeated many times 3006, and the fluorescence radiation can be accumulated by a microscope camera or detector. If there are many such fluorescent molecules 3001 within a diffraction limited resolution volume (“DLRV”) of the imaging optics it might seem difficult to distinguish the fluorescence radiation of one molecule from another molecule.

[0168] However, in the case of a phototransformable optical label (“PTOL”) molecule or emitter 3011, the ability of the PTOL to absorb excitation radiation and therefore to emit fluorescence radiation can be explicitly turned on by an activating signal, and in certain cases, can be turned off by a de-activating signal. In an inactivated state, a PTOL 3011 can be exposed to excitation radiation 3012 having a characteristic wavelength, but it will radiate little, if any, fluorescence radiation at a wavelength characteristic of an activated and excited PTOL. However, when the PTOL 3021 is irradiated with activation radiation 3022, the PTOL 3021 can be transformed into an excitable state 3023. The activation radiation 3022 often has a different wavelength than the wavelength of the excitation radiation, but for some PTOLs activation radiation and excitation radiation have the same wavelength and are distinguished by their intensities. After a PTOL is transformed into an excitable state 3023, subsequent illumination of the activated PTOL 3023 by excitation radiation 3024 generally results in detectable emission of fluorescence radiation 3026. This process of excitation and emission can be repeated numerous times 3028 for an activated PTOL 3027 until the PTOL eventually bleaches or deactivates, at which point the PTOL 3029 can no longer be excited and can no longer emit fluorescence radiation.

[0169] Thus, a PTOL 3021 can be illuminated with activation radiation 3022 to transform the PTOL into an activated state 3023. The activated PTOL 3023 can be illuminated with excitation radiation 3024 to excite the PTOL into an excited state 3025, from which the PTOL 3025 can emit radiation 3026. For some species of PTOL, the PTOL can be transformed from an activated state 3023 back to an unactivated state 3021, either through spontaneous decay to the unactivated state or through the application of de-activation radiation.

[0170] A fluorescent protein (“FP”) is a particular kind of phototransformable optical label (“PTOL”) whose optical properties can be altered by light and that can be used to label a portion of a sample to optically image the portion of the sample. As used herein “fluorescence” and “fluorescent” generally designate an optical response of the PTOL. In addition to the common understanding of fluorescence (e.g., emission of a photon from a substance in response to excitation by a more energetic photon) we include other properties that can characterize the PTOL, such as, for example, emission of a photon in response to multi-photon excitation, or a large elastic optical cross section that can be activated or deactivated.

[0171] PTOLs useful for superresolution via localization of isolated PTOLs generally can have one or more of the following distinguishing characteristics: a relatively high brightness (as defined by its excitation cross section and the quantum efficiency); a relatively high contrast ratio between luminescence generated in the activated state to that generated in the inactivated state (which might be improved through a judicious choice of the excitation wavelength and detection filter set); an excitation wavelength that reduces autofluorescence from other cellular material exposed to the excitation; an emission wavelength that is sufficiently different from the spectral range over which most autofluorescence occurs; and photostability that is large enough that a sufficient number of photons are collected from each PTOL to achieve the desired localization accuracy prior to irreversible bleaching, yet, for PTOLs other than the kindling proteins and Dronpa that can switch back to the deactivated state, is nevertheless still finite, so that a new population of individually resolvable activated PTOLs can be created after the current set is largely bleached. Indeed, to reduce possible phototoxicity related to irreversible photobleaching, an ideal PTOL would remain in the activated state until it is deactivated by choice using other means (e.g., illumination at a separate deactivation wavelength).

[0172] Photoactivatable fluorescent proteins useful for superresolution microscopy can include, for example, Aequorea victoria photoactivated green fluorescent protein (“PA-GFP”), Photoswitchable cyan fluorescent protein (“PS-CFP”), Kaede, Kindling fluorescent proteins (“KFP”), and Dronpa. Superresolution via localization has been demonstrated with the tetrameric PTOLs Kaede and Kikume, as well as the monomeric, dimeric, and tandem dimer forms of EosFP. These PTOLS have the common advantages of large wavelength spread between the inactivated and activated absorption and emission maxima, high brightness, and longer wavelength emission, where autofluorescence is typically lower. Monomeric EosFP has the added advantage of smaller physical size than tetrameric Kaede or Kikume, and may therefore be less perturbative of cellular structure and function. In practice, a particular FP could be selected from a number of different FPs based on a user's criteria for optimization for a given application. Given the diversity of PTOL species with different activation, excitation, and emission wavelengths and time constants, it is possible to construct separate images for each species of PTOLs. Thus, different components of a sample can be tagged with distinct labels, and each labeled object can then be independently identified in a super-resolution image that can be constructed as disclosed herein.

[0173] It is possible to label specific sample features of interest with PTOLs, such that the PTOLs, and therefore the specific sample features, can be imaged. For PTOLs that can be genetically expressed (e.g., photoactivable fluorescent proteins), DNA plasmids can be created and inserted into the cell by transient transfection, so that fluorescent protein PTOLs are produced fused to specific proteins of interest. Likewise, stable transfections that permanently alter the genetic makeup of a cell line can be created, so that such cells produce fluorescent protein PTOLs. PTOLs also can be tagged to specific cellular features using immumolabeling techniques, or high-specificity small molecule receptor-ligand binding systems, such as biotin ligase.

[0174] Radiation from molecules or emitters can be used for sub-diffractive localization of PTOLs when the radiating molecules or emitters are isolated and spaced further apart from each other than the diffraction limited length scale of the imaging optics. For example, as shown in FIG. 31, excitation radiation 3101 can excite an isolated emitter 3102 into an excited state 3103. Outgoing radiation 3104 emitted from the excited emitter 3103 can be collected by microscope optics including a detection objective 3105 and refocused 3106 onto a diffraction limited spot 3107. This spot profile is shown plotted on the axis of position 3108 versus emission intensity 3109 in the image plane 3108. The image and object plane are scaled by the magnification M. In the image plane 3108, the minimum spatial width of this spot is characterized by a fundamental limitation of resolution of microscopes and is given by the Abbe criteria Δx≈0.5*λ*M/NA, where λ is the wavelength of emission radiation 204 and NA is the numerical aperture of the objective 205. One can use this magnified image of the isolated emitter to localize the emitter to sub-diffractive precision by measuring the distribution of the emission at a detector such as a CCD camera. This data can then be fit or otherwise processed to find the center of the detected signal. For example, the emission intensity profile of light emitted from a PTOL and detected on a detector can be characterized by the discrete data set, {n_i,}, where n_i are the number of photons detected in the i^th pixel of the detector located at position x_i. This data can be fit to a peaked function to determine a location of the PTOL. For example, a Gaussian function,

$E_{\mathrm{tot}}\left(x,z\right)=\sum _{n=1}^N\exp \left(n\alpha \right)E_b\left(x+nT,z\right)$

can be used to perform the fit. A least squares fit of the data to the peaked function, for example, can find a value for the peak center location x_c. In addition other parameters, such as, for example, the total number of photons detected, N, and the peak width, σ (which can be generally on the order of Δx) can also be deduced from the fit. Errors in n_i can be expressed by a value, δn_i, and likewise the uncertainty in the center position, x_c, can be expressed as through a parameter, δx. In particular, when the system noise is limited by photon shot noise statistics (meaning δn_i=sqrt(n_i)) arising from the detected signal and N is the number of photons detected, then the accuracy to which this center can be localized is given by δx=Δx/sqrt(N). To the extent that N is much larger than unity, the localization accuracy 3110 can be significantly better than the diffraction limit 3121. The data also can be fit to other functions than the Gaussian function to determine a center location and width of the position of a PTOL.

[0175] However, it can be difficult to apply this technique to a set of continuously-emitting fluorescent molecules 3112 that are spaced so closely together that they are within Δx of each other. In this case, the diffractive spots are highly overlapped, such that fitting of the image of a molecule to obtain a position of the molecule with superresolution accuracy is difficult. Thus, in this situation the resolution limit generally is given by standard Abbe criterion 3121, i.e. the width of the diffractive limited spot.

[0176] However, by selectively activating and de-activating subsets of PTOLs within a dense set of PTOLs this localization concept can be used even when the optical labels are closely spaced. As shown in FIG. 32, when weak intensity activation radiation 3201 bathes closely spaced PTOLs 3202 a small, statistically-sampled fraction 3203 of all the PTOLs absorbs the activation radiation and is converted into a state 3203 that can be excited by the excitation radiation 3204. The emission radiation 3205, 3207 from this activated and excited subset is focused to a set of isolated, diffraction limited spots 3208 whose centers can be localized to sub-diffractive resolution 3209 as illustrated previously in FIG. 31. After enough photons are collected to generate sufficiently resolved images of the PTOLs that are members of the activated and excited subset, the activated PTOLs are either deactivated to return to an activatable state 3202 (as in the case of Dronpa or KFP) or are permanently photobleached to a dark form 3213, effectively removing them from the system. Another cycle of weak intensity activation radiation 3211 is then applied to activate a new subset 3216 of the remaining activatable PTOLs 3212. The PTOLs in this second subset in turn can be put into the excited state 3217 by excitation 3215. The radiated light 3218, 3220 is refocused by the microscope lens 3219 onto well-separated diffractive resolution limited spots 3221. Once again, fitting of each peak can define the sub-diffractive locations 3222 of the PTOLs in the second subset. Further cycles will extract sub-diffractive locations of other PTOLs, such as PTOL image locations 3223.

[0177] As shown in FIG. 33, multiple sub-diffractive resolution images in two spatial dimensions, x and y, of individual PTOLs in a sample can be generated, and then the multiple images can be combined to generate a sub-diffraction limited resolution image of an x-y plane of the sample. An initial image of a few discrete PTOLs emitting at a wavelength that is imaged by imaging optics is shown in frame 3301. After a subset of PTOLs is activated with an activation pulse of radiation having an activation wavelength different from the wavelength of radiation that is imaged, more PTOLs are detected, as shown in frame 3302. Several such frames are recorded until many of these initially-activated PTOLs bleach and can no longer emit, as shown in frame 3303. At this point, a new activation pulse can convert a new subset of PTOLs into an activated state, and this new subset of PTOLs can emit radiation at the imaging wavelength when the newly-activated PTOLs are excited, which results in the image of frame 3304. This cycle can be repeated to generate several hundred or thousands of such image frames, which can be considered to represent a 3D data stack 3305 of PTOL images, with the coordinates, x and y, on the horizontal plane and the time, t, on the vertical axis. Then all these individual image frames in the data stack can be summed to generate a total image that is equivalent to a long time exposure of a diffraction-limited image from a microscope, as shown in frame 3306.

[0178] When activated PTOLs are sufficiently sparse in the sample, the raw signal from each activated PTOL (e.g., the intensity of the signal on individual pixels of a CCD detector), as shown in frame 3307, can be fitted with an approximate point spread function (e.g., a Gaussian) to generate a smoothed, fitted signal, as shown in frame 3308, and the center x,y coordinates of each PTOL can be determined. The location of each PTOL can then be rendered in a new image as a Gaussian centered at the measured localization position, having a width defined by the uncertainty to which this location is known. This uncertainty can be significantly less than the original radius of the original, diffraction-limited PTOL image 3307 (typically by an approximate factor of sqrt(N), where N is the number of photons detected to generated the image of the PTOL). For example, if there were 3300 photons in the pixels of the image spot of a PTOL, the uncertainty of the fitted central location can be 1/20 of the size of the original diffraction limited image of that PTOL.

[0179] Applying this process to images of all the activated PTOLs in frames 3301, 3302, 3303, and 3304 leads to the corresponding narrow rendered peaks in frames 3310, 3311, 3312, and 3313. The widths of these rendered peaks are given by their localization uncertainty. Applied to all activated PTOLs in all frames of the data stack 3305, this localization process results in a list of coordinates for many PTOLs within the sample. Alternatively, the rendered peaks can be accumulated (e.g., summed) to give a superresolution image 3314 of a dense set of PTOLs. The emission of any activated PTOL may persist over several frames until it is bleached or otherwise deactivated. For such a case, an implementation of this accumulation is to identify the coordinates across several frames of what is likely to be a common PTOL. This set of coordinates can be averaged or otherwise reduced to obtain a single, more accurately localized coordinate vector of that PTOL. A comparison of the diffraction limited image 3306 and the superresolution image 3314 illustrates the higher resolution achievable by this process.

[0180] This process of serial activation of different isolated PTOL subsets allows an effective way of localizing the positions of a dense set of PTOLs, such that superresolution images in 1, 2, or 3 spatial dimensions can be generated, as described in more detail herein. Furthermore, this process can also be independently repeated for different species of PTOLs within a sample, which have different activation, excitation, and/or emission wavelengths. Separate or combined superresolution images can then be extracted using each PTOL species. The extracted positional information of two or more different PTOLs that label two different binding proteins can describe co-localization and relative binding positions on a common or closely connected target. This can be useful for determining which proteins are related to each other.

[0181] FIG. 34 is a flow chart of a process 3400 for creating an image of a sample containing multiple relatively densely-located PTOLs. Activation radiation having an activation wavelength can be directed onto a sample to transform a subset of PTOLs in the sample from an unactivated to an activated state (step 3402). Excitation radiation is applied to activated PTOLs in the sample at the excitation wavelength, and radiation that is emitted from activated and excited PTOLs and incident onto the imaging and detecting optics is acquired and saved (step 3403). Images of a set of activated PTOLs can be acquired and saved multiple times. For example, the controller can require that N images of a set of activated PTOLs are acquired, such that if N images have not yet been acquired (step 3404) image acquisition (step 3403) is repeated. The excitation radiation can be applied to the sample continuously or can be switched off between acquisitions of images.

[0182] After N images of the subset of activated PTOLs are acquired, and if more images are to be obtained from the sample (step 3405) another activation pulse can be applied to the sample to activate another set of PTOLs (step 3402). Excitation radiation can be applied to this other set of activated PTOLs, and radiation emitted from the activated and excited PTOLs can be acquired and saved (step 3403). Multiple sets of PTOLs can be activated. For example, the controller can require that M sets PTOLs be activated, such that if M sets have not yet been activated (step 3405) another activation pulse is applied (step 3403). Thus, the process of activating a set of PTOLs, exciting PTOLs within the activated set, and acquiring images from the activated and excited PTOLs can be repeated multiple times, for example, until the total pool of available PTOLs becomes exhausted or until a desired number of images of a desired number of different PTOLs within a spatial area or volume is achieved.

[0183] While applying the activation and excitation radiation, the number of iterations N between activation pulses, along with the intensity of the activation and excitation radiation can be controlled such that the mean volume per imaged PTOL in an individual image is generally more than the DLRV of the optical imaging system used to detect and localize the individual PTOLs. The density of activated PTOLs that are capable of emitting radiation is generally highest in images acquired immediately after the activation pulse and generally decreases as more PTOLs photobleach during the acquisition of the N image frames.

[0184] Furthermore, as the process 3400 progresses, and the number of activation pulses increases from 1 to M, PTOLs within the sample may photobleach, such that fewer and fewer PTOLs within the sample are available to be activated, excited, and imaged. Thus, in one implementation, the intensity and time length of individual activation pulses and the intensity and time length of excitation radiation can be controlled, to reduce the variation in density of activated PTOLs as the process progresses. For example, using less excitation radiation (possibly with fewer frames N between activation pulses) can reduce the decrease in imaged PTOLs from the first frame after an activation pulse to the N^th frame just preceding the next activation pulse. In another example, the intensity of individual activation pulses can increase as the process 3400 progresses from the first to the M^th activation pulse. This would reduce the decrease in the number of imaged PTOLs in the first acquisition frame after the M^th activation pulse relative to the number of imaged PTOLs in the first acquisition frame after the first activation pulse, thereby compensating for the reduction in the number of activable PTOLs as the sequence of activation and image acquisition progresses. Thus, in the first example, the variation of activated and excitable PTOLs during an excitation sequence is reduced, and in the second example, the variation of activated and excitable PTOLs during the activation sequence is reduced. The reduced variation of activated and excitable PTOLs allows operation, where more PTOLs can be localized per unit time, while not exceeding the density criteria of more than one imaged PTOL per DLRV.

[0185] In one implementation, multiple species of PTOLs within the sample can be activated, excited, and imaged. For example, steps of applying the activation pulses (3402) and of exciting and imaging (3403) can include applying pulses of activation radiation and excitation radiation, respectively, having wavelengths corresponding to the different activation and excitation wavelengths of different PTOL species. A multiplicity of detectors and/or filters can also be used in the imaging step 3403 to image different wavelengths of radiation emitted from different PTOL species. In this manner, multiple independent data sets of images can be acquired. These independent data sets in turn can be reduced to corresponding super-resolution images of each PTOL species within a sample.

[0186] If the contrast ratio between activated and inactivated PTOLs is too low at a given initial density of target PTOLs to achieve the desired SNR and consequent localization accuracy, the contrast ratio can be improved by irreversibly bleaching a portion of the target PTOLs until the effective molecular density and resulting SNR is as desired. Other autofluorescent material in the sample can also be pre-bleached using the excitation light without affecting the bulk of the inactivated PTOLs. Further discrimination with respect to background might be obtained via appropriate spectral filtering, fluorescence lifetime measurements, or polarized excitation and/or polarization analyzed detection.

[0187] FIG. 35 is a schematic view of a system 3500 that can be used to implement the techniques described herein. The system 3500 is similar to the system 1900 also includes can include a source 3502 of the activation radiation in addition to the source 1902 of excitation radiation. The activation radiation can be coupled into the beam path of the excitation radiation through the use of a beam splitter 3504 positioned between the source of excitation radiation 1902 and the lens 1904A. As shown in FIG. 35, in some implementations, the beam paths of the excitation radiation and the activation radiation can overlap and can be directed to the sample 1946 by at least some of the same beam-forming optics (e.g., galvanometer-mirrors 1928 and 1936, wavefront modulator 1912, etc.). The activation radiation and/or the excitation radiation can be provided to the sample in the form of a thin sheet of light, e.g., a plane or a structured illumination or a lattice light sheet or one or more swept Bessel-like beams.

[0188] In other implementations, the excitation radiation in the activation radiation may be provided to the sample 1946 from different directions. For example, the activation radiation may be provided to the sample 1946 through the detection objective 1948, and the excitation light may be provided a thin sheet at the focal plane of the detection objective. In other implementations, the beam splitter 3504 that couples the activation radiation and the excitation radiation may be provided in a different position along the beam path shown in FIG. 35. For example, the beam splitter may be located between relay lens 1940 and excitation objective 1942, and the beam path for the activation radiation may include independent beam-forming optical elements to shape and direct the activation beam.

[0189] The light source 3502 can be directly modulated, or modulated via a shutter 3506 placed in the beam path of the activation radiation emitted by the light source 3502. The shutter can operate to admit or prevent activation radiation from passing from the light source 3502 to the sample 1946. In one implementation, the shutter can be a mechanical shutter that moves to selectively block the beam path. In another implementation, the shutter can be a material that can be modified electronically or acoustically to admit or prevent light from passing or to alter a beam path from the light source 3502. Similarly, excitation radiation that causes an activated PTOL to be transformed from a de-excited state to an excited state can also be passed from an excitation light source 1902 through a shutter 3512 to the sample 1946.

[0190] A controller (e.g., a general or special purpose computer or processor) can control one or more optical elements of the systems 1800, 1900, 3500. For example, a controller can be used to control parameters of the activation and excitation radiation (e.g., the wavelength, intensity, polarization, and duration of pulses of various radiation beams that reach the sample 1946, 3501; and the timing of activation radiation pulses and excitation radiation pulses) during an image acquisition sequence. Of course, the optical elements can be arranged in other configurations. Data from images formed at the detector 1953 are communicated to a controller for storage and processing. For example, the controller can include a memory for recording or storing intensity data as a function of position on the detector for different image frames. The controller can also include a processor for processing the data (e.g., a general or special purpose computer or processor), for example, to fit the data recorded for an image of an individual PTOL to determine a location of the PTOL to sub-diffraction limited precision, or to combine the data about the locations of multiple PTOLs that are determined with superresolution accuracy to generate an image of the sample based on the locations of multiple PTOLs that have been located with superresolution accuracy.

[0191] Thus, in some implementations, the sample 1946 can include a dense plurality of photo transformable optical labels. The density of the optical labels in the sample can be greater than an inverse of the diffraction limited resolution volume of the detection optics of the system. Activation radiation can be provided to the sample to activate a statistically sampled subset of the labels in the sample. For example, the source 3502 can generate a beam of activation light having a first wavelength, and the activation light can be steered to the sample by optical elements shown in system 3500.

[0192] In some implementations, the activation radiation can be provided in the form of one or more Bessel-like beams that are swept, stepped, or dithered in a direction having a component orthogonal to the propagation direction of the Bessel-like beam and having a component orthogonal to an optical axis of the detection objective 1948. In some implementations, the activation radiation can be provided in the form of an array of incoherent Bessel-like beams that are swept, stepped, or dithered in a direction having components that are orthogonal both to the direction of propagation of the Bessel-like beams and orthogonal to an optical axis of detection objective 1948. In some implementations, the activation radiation can be provided in the form of an array of coherent Bessel-like beams that are swept, stepped, or dithered in a direction having components that are orthogonal both to the direction of propagation of the Bessel-like beams and orthogonal to an optical axis of detection objective 1948. In some implementations, the Bessel-like beams of the array can be phase coherent with each other. In some implementations, the Bessel-like beams in an array of beams can partially overlap with neighboring beams in the array within the sample. In some implementations, the activation radiation can be provided in the form of a Gaussian-like beam that is swept, stepped, or dithered in a direction having a component orthogonal to the propagation direction of the Bessel-like beam and having a component orthogonal to an optical axis of the detection objective 1948. The sweeping, stepping, and/or dithering of the beam(s) of activation radiation can form a thin sheet of activation radiation near a focal plane of the detection objective 1948. In some implementations, the activation radiation can be provided in the form of a static thin sheet of activation radiation in a plane substantially perpendicular to the optical axis of the detection objective 1948. For example, the thin sheet of activation radiation can be formed through use of a cylindrical lens used to focus the activation radiation in one spatial direction. In some implementations, the activation radiation is not provided in the form of a thin light sheet, but rather provided through widefield techniques. The activation radiation can be controlled such that the density of activated labels in the subset is less than the inverse of the diffraction limited resolution volume of the detection optics. For example, the intensity of the activation radiation and/or the time for which the activation radiation is provided to the sample can be controlled such that the probability of the activation radiation activating a label convoluted with the density of the labels in the sample is such that the resulting density of activated labels is less than the inverse of the diffraction limited resolution volume of the detection optics.

[0193] Once the subset of activated labels is created, a thin sheet of excitation radiation can be provided to the at least some of the activated labels in the sample to excite at least some of the activated photo transformable optical labels. For example, the source 1902 can generate a beam of excitation light having a second wavelength, and the excitation light can be steered to the sample by optical elements shown in system 3500.

[0194] In some implementations, the excitation radiation can be provided in the form of one or more Bessel-like beam that are swept, stepped, or dithered in a direction having a component orthogonal to the propagation direction of the Bessel-like beam and having a component orthogonal to an optical axis of the detection objective 1948. In some implementations, the excitation radiation can be provided in the form of an array of Bessel-like beams that are swept, stepped, or dithered in a direction having components that are orthogonal both to the direction of propagation of the Bessel-like beams and orthogonal to an optical axis of detection objective 1948. In some implementations, the Bessel-like beams can be phase coherent with each other. In some implementations, Bessel-like beams in an array of beams can partially overlap with neighboring beams in the array within the sample.

[0195] In some implementations, the excitation radiation can be provided in the form of a Gaussian-like beam that is swept, stepped, or dithered in a direction having a component orthogonal to the propagation direction of the Bessel-like beam and having a component orthogonal to an optical axis of the detection objective 1948. The sweeping, stepping, and/or dithering of the beam(s) of excitation radiation can form a thin sheet of excitation radiation near a focal plane of the detection objective 1948. In some implementations, the excitation radiation can be provided in the form of a static thin sheet of excitation radiation in a plane substantially perpendicular to the optical axis of the detection objective 1948. For example, the thin sheet of excitation radiation can be formed through use of a cylindrical lens used to focus the excitation radiation in one spatial direction.

[0196] Radiation emitted from the activated and excited labels is imaged by imaging optics, including the detection objective 1948, onto a detector 1953. The detection objective has an axis along a direction that is substantially perpendicular to the sheet of excitation radiation. Locations of labels from which radiation is detected can be determined with super resolution accuracy by one or more processors or computing devices based on the detected radiation. The process of activating a statistical subset of transformable labels, exciting the activated labels, and detecting light from the activated and excited labels can be repeated, where different subsets of transformable labels are activated during different rounds of activation. Finally, a sub-diffraction-limited image of the sample can be generated by one or more processors of a computing system based on the determined locations of the labels.

[0197] Other planes of the sample 1946 can be imaged by moving the activation radiation and the excitation radiation and the focal plane of the detection objective 1948 to different positions within the sample. For example, in one implementation, the sample can be mounted on a movable stage 3506 that is configured to change the position of the sample with respect to the focal plane of the detection objective 1948. In another implementation, the activation radiation and the excitation radiation can be steered to different planes along the axial direction of the detection objective by the beam-forming optics of the system 3500 (e.g., by galvanometer-mirror 1928). When the activation and excitation radiation beams are steered to different positions within the sample, the focal plane of the detection objective can be changed correspondingly, such that committing optical labels from the newly positioned plane of excitation radiation can be imaged effectively by the detection objective 1948. When optical labels in different planes of the sample are activated, excited, and imaged, the locations of the optical labels in the different planes can be combined to generate a three-dimensional image of the sample.

[0198] As explained herein, in PAINT microscopy, the density of signal-emitting labels can be increased by utilizing freely diffusing probes (i.e., optical labels) that possess an affinity—either inherent or through incorporation of a peptide tag (e.g., Halo-tag or SNAP-tag)—to a given structure. The probes can be suspended in a buffer solution (e.g., phosphate buffer saline solution) that bathes the sample of interest, and probes can diffuse onto the sample or into the sample and tag the structures for which they possess an affinity. Probes can be developed to have an affinity for different structures, so that the different structures can be labeled by the different probes, and then by detecting the light from the probes that stick to the different structures an image of the structures can be created. Probes that stick to a structure can be localized in space, so that light received from the stuck probe over an integration time of the detector is all received at the same location on the detector, resulting in a strong signal at the location on the detector, while probes the diffuse through sample during the integration time of the detector may contribute only a weak signal, which may be below a threshold level, at different locations on the detector. Different probes can be applied sequentially to create images of different structures for which the probes have an affinity, and after an image is created using one type of probe, the probes can be washed away, and then a new type of probe that has an affinity for a different structure can be introduced to create an image of the different structure of the sample.

[0199] By controlling the density of these molecules in the bulk solution and the exposure time for a single camera acquisition, only stably-bound molecules will contribute significant signal so that their positions can be localized, whereas freely diffusing molecules will only contribute a uniform background. Probes that bind to the structures of interest emit fluorescence signal light when excited by excitation light, and the fluorescence signal is detected and then used to localize the probes, and the localization information is used to generate an image of the structures that are tagged by the probes. Eventually, a bound probe either becomes unbound from the structure or becomes bleached by the excitation light, at which point the probe ceases to contribute signal light that can be used to localize the probe. However, because the sample is bathed in a solution that contains additional PAINT probes, a constant source of new molecules is present in the bulk solution, and the source of new molecules can assure that, over time, a high number of available binding sites can be labeled.

[0200] However, when using PAINT microscopy with a widefield microscope, the concentration of the fluorescent molecules in the bulk solution must be kept low enough so that the background contributed by the out-of-focus fluorophores (from both the out-of-focus stably bound and the freely diffusing fluorophores) does not overwhelm the signal from in-focus, stably bound fluorophores to a degree that hinders the localization of the in-focus fluorophores. In addition, because both widefield microscopy and confocal microscopy illuminate the entire thickness of the sample, but detect fluorescent molecules only from a two-dimensional plane that is in-focus, a substantial portion of the out-of-focus molecules in solution are bleached before ever being localized.

[0201] To address these issues of background light, fluorophores at, or near, the focal plane of the detection objective can be illuminated with a sheet of excitation light, as described herein, while fluorophores that are not at, or near, the focal plane of the detection objective are not illuminated with excitation light. While a thin slice of the sample corresponding to the plane at, or near, the focal plane of the detection objective is illuminated by the sheet of excitation light, PAINT microscopy can be performed to localize molecules within the slice. The sheet of excitation light can be scanned through the sample while PAINT microscopy is performed to localize molecules within different slices of the sample, and a three-dimensional image of the sample can be generated from the information about the localized molecules within the sample.

[0202] The sheet of excitation light can have a thickness along the Z-axis (i.e., parallel to the optical axis of the detection objective) that is approximately comparable to, or that is thinner than, the depth of focus of the detection objective. In some implementations, the sheet of excitation light can be formed from one or more or Bessel-like beams or from a plane of structured illumination (e.g., a lattice light sheet).

[0203] In some implementations, the sheet of excitation light can be provided by lattice light sheet microscopy, in which the sheet of excitation light illuminates the sample through a second objective oriented orthogonal to the detection objective. In some implementations, the sheet of excitation light can be a bound, two-dimensional optical lattice. In contrast to methods that use Gaussian light sheets with a full width at half maximum (FWHM) of several microns, the lattice light sheet (e.g., a thin sheet of light formed by a superposition of beams, where the superposition forms an optical lattice) can have a FWHM thickness (i.e., the thickness of the sheet over which the intensity of the light is within 50% of the maximum intensity) of approximately 1 μm or less and can be sufficiently thin compared to the depth of focus of a high NA (e.g., >1.0) detection objective to illuminate only in-focus molecules, while still having a Rayleigh length comparable to the aforementioned Gaussian beam. Because in-focus molecules are preferentially illuminated by the excitation light, a higher concentration of fluorescent molecules in bulk solution can be used in PAINT microscopy without background fluorescent light from out-of-focus molecules overwhelming the signal from the in-focus molecules. Thus, densely fluorescent and thick samples can be imaged faster than would be possible using widefield, confocal, or Gaussian light sheet microscopy because those techniques are subject to significant background from the fluorescing PAINT probes that are not located at or near the focal plane of the detection objective.

[0204] The sample can be scanned repeatedly (e.g., via a piezo-electric actuator) through a plane that contains both the focal plane of the detection objective and the lattice light sheet of excitation light. In each scan location, stably-bound fluorescent molecules in the sample can be localized in three-dimensions. The Z-axis position, parallel to the optical axis of the detection objective, of a PAINT probe can be determined by utilizing techniques that rely on a z-axis-dependent aberration of the detected light (e.g., an astigmatic detection point spread function (PSF) and a previously measured calibration curve, or a double-helix point spread function, or a biplane imaging system). The X-axis and Y-axis positions of the molecules can be determined by statistical analysis of the detected light in the X-Y plane (e.g., by determining a centroid of the detected light in the X-Y plane).

[0205] Generally, the gradient of the Z-axis-dependent aberration of detected light can occur over a length in the Z-axis direction that is comparable to the depth of focus of the detection objective. The gradient of the Z-axis-dependent aberration of the detected light (e.g., the gradient of the astigmatism used) can be selected to provide a desired degree of resolution along the Z-axis. For example, by using a relatively aggressive astigmatism, the localization of the PAINT probes can be relatively high.

[0206] Acquiring sufficient localization data from the sample to generate a super resolution image of the sample may occur over a time period (e.g., hours, days, weeks) during which the sample changes shape, changes size, or moves, where such changes in movements of the sample are collectively referred to as “drift” of the sample. Sample drift may occur as a result of the non-equilibrium conditions in which the imaging occurs, because the sample continuously absorbs PAINT probes that diffuse into the sample

[0207] In some implementations, PAINT microscopy can be performed under non-equilibrium conditions. For example, if the labels bind permanently rather than transiently, then the sample can be progressively perturbed as additional dye molecules bind to it, and when imaged over many hours the sample can swell as more and more labels bind to the sample. If left uncorrected, this swelling can dramatically reduce the precision of the registration of molecules localized at different times, and thus the resolution of the final image. This swelling effect would also be expected to occur with any exogenous labeling strategy, including heavy metal staining for EM. However, because conventional super-resolution microscopy and EM are performed after pre-labeling, the deformation would not further manifest itself during imaging. Thus, in some implementations, correction for translational drift alone may not be sufficient to correct for the more complex non-linear deformations exhibited by thicker 3D specimens in PAINT.

[0208] Therefore, to mitigate the effects of the sample drift and sample deformation on the resolution of features within the sample, three-dimensional subimages of the sample can be generated from localization data acquired over a time period that is relatively short compared to the time required to acquire all of the localization data, and then the different subimages can be registered to each other. The registration can be performed using a three-dimensional, non-linear fitting process based on the location of fiducial markers (e.g., gold nano beads) embedded in a cover slip that supports the sample or based on features within the sample itself. For example, three-dimensional subimages of the sample can be generated based on localization data acquired over a time period on the order of hours (e.g., one hour, two hours, four hours, eight hours, etc.), when the total acquisition time is on the order of days or weeks. In some implementations, the entire localization data set can be divided into a plurality of subsets, and then low-resolution, three-dimensional sub images can be plotted from each subset. Once the different subimages are registered in three dimensional space on top of each other, then localization data for a plurality of the subimages (e.g., all of the subimages, except for subimages that include obvious errors) can be integrated, and a super resolution image of the sample can be generated from the integrated data. By using the three-dimensional, non-linear fitting process to perform drift correction, high-resolution images of relatively thick samples can be obtained, despite the relatively long localization data acquisition time for thick samples compared to thin samples and the larger drifts encountered by thick samples than by thin samples.

[0209] In some implementations, the registration based on fiducial-based translational registration, non-linear image transformation, or a combination of the two can be performed using a symmetric diffeomorphic image registration (SyN) algorithm, for example, a SyN algorithm available through the open source Advanced Normalization Tools (ANTs). For example, for each sample, sub-images can be generated from molecules localized over a plurality of volume acquisitions (e.g., 5000 volume acquisitions at, for example, 100 nm voxel dimensions), and used to represent the geometry of the specimen at a given time point. Each of these sub-images can be registered to a template image, for example, using the first or last time point obtained for a given label, to generate a continuously differentiable deformation function. These deformation functions then can be linearly interpolated over space and time for all molecule localizations before rendering a final high-resolution image. Analysis of the nonlinear swelling correction suggests an accuracy of approximately 20 nm in each of the x, y, and z axes when estimating the true location of a given optical label localization, even when correcting for several hundred nanometers of swelling of the sample.

[0210] Thus, the 3D positions of different fluorescent molecules within the sample can be linked across multiple images and registered in three dimensions, while accounting for motion of the scanning piezoelectric actuator and then re-plotted in three dimensions as Gaussian spots whose dimensions are determined according to the localization precision. A superresolved image of the sample can be constructed from the sum total of these reconstructed spots.

[0211] In some implementations, the light sheet of excitation light and the detection objective focal plane can be moved within the sample along the z-axis in steps that are less than the resolution limit of the detection objective. For example, the light sheet and focal plane can be moved along the Z-axis in steps that are one-third of the resolution limit of the detection objective along the Z-axis. Then, multiple localizations can be obtained for molecules that remain stationary and emit fluorescence light while the light sheet and detection objective focal plane is stepped along the Z-axis before the emitting molecule either diffuses away from its position or bleaches. When imaging an emitting molecule with an astigmatic detection PSF and by obtaining localizations of the molecule as the light sheet and detection objective focal plane is scanned in the Z-direction, the localization of the molecule can be higher in the X, Y, and Z directions than if the molecule produced fluorescence light only for a single z-axis position of the light sheet.

[0212] Because the PAINT probes must be transported from the bulk solution into the sample by diffusion, relatively long times may be required for probes to diffuse into the bulk of a thick sample. Furthermore, to allow a sufficient density of probes to diffuse to the interior of the sample without being bleached before they reach the interior, so that they can be used to generate localization data structures within the interior of the sample, the intensity of excitation light must be kept below a threshold value, which limits the rate at which localization data can be acquired. To increase the diffusion rate of the PAINT probes, and thereby increase the acquisition rate of localization data, it can be desirable to use low molecular weight probes or it can be desirable to hold the sample and the bulk solution containing the probes at an elevated temperature above room temperature.

[0213] In some implementations, different features within a sample can be imaged with the same optical elements (e.g., with the same microscope) but with using different probes to image different features of the sample. For example, stochastic imaging techniques (e.g., PALM, STORM) can be used to image a first features within a sample (e.g. a biological sample, such as, a cell), and then PAINT techniques can be used to image other features within the sample. For example, with PALM, endogenously expressed fluorophores within the sample can be used to tag structures of interest within the sample and provide fluorescence light from the tag structures, while STORM uses immunolabeling of the sample with antibodies tagged with organic fluorophores. Thus, stochastic imaging techniques can be used to label endogenous material within the sample, such as, for example, nuclear membranes of a cell or protein-specific structures within a cell.

[0214] In both PALM and STORM, fluorophores are stochastically switched from a state in which they do not readily emit fluorescence light in response to excitation light to a state in which they do readily emit fluorescence light in response to excitation light. Because of the stochastic switching, very closely spaced molecules that reside in the same diffraction-limited volume (and which would be indistinguishable with a widefield microscope) can be localized with super resolution accuracy by acquiring signal light from the different molecules at different times during the data acquisition process.

[0215] PAINT techniques can be used to label additional structures of the sample. PAINT probes can include either of dyes with inherent affinity for a biological target, such as Nile Red to stain the plasma membrane, or fluorophores attached to affinity reagents, such as antibodies for transmembrane proteins. For example, a first PAINT probe can have a specific affinity for intercellular membrane structures of cells, and another PAINT probe can have a specific affinity for DNA, and another PAINT probe can have a specific affinity for plasma membranes of cells. To find inherent binders, we screened a library of rhodamine dyes with different N-substitution patterns and looked for selective staining patterns in fixed cells by fluorescence microscopy. We observed that a rhodamine derivative bearing 7-membered azepane rings stained the intracellular membrane system. This selective binding may be due to the balance between the water-soluble zwitterionic rhodamine system and the lipophilic azepane rings. To engineer a directed affinity PAINT probe, we synthesized a conjugate of Janelia Fluor 646 attached to Hoechst 33258 through a short polyethylene glycol linker (Hoechst-JF646). The Hoechst moiety ensured binding to AT-rich DNA sequences and the environmental sensitivity of JF646 caused a >50-fold increase in fluorescence upon binding.

[0216] Different PAINT probes can be introduced sequentially through the buffer solution that is flowed over the sample, and images of the sample can be obtained while the different PAINT probes diffuse into the sample. That is, a first PAINT probe can be introduced through the buffer solution to the sample and used to obtain a super resolution image of structures tagged by the first probe, and then the first probes can be flushed from the sample, and a second PAINT probe can be introduced through the buffer solution to the sample and used to obtain a super resolution image of different structures tagged by the second probe. This process can be needed for additional different PAINT probes to produce additional images of different structures of the sample.

[0217] In this manner, a first image of the sample can be obtained based on the signal light emitted from endogenously expressed fluorophores (using PALM) or from antibodies tagged with organic fluorophores (using STORM), where the first image provides information about the structures that bind the fluorophores. Then, additional images of the sample can be obtained based on signal light emitted from different PAINT probes that have different affinities for different structures of the sample, where the additional images provide information about the structures that bind the different PAINT probes. The different images of the sample can be correlated with each other (e.g., based on fiducial markers or based on native structures of the sample that appear in each of the different images) and then combined to create an image of the sample that contains information obtained from the different labels.

[0218] In some implementations, PAINT probes that normally are not fluorescent, but that become fluorescent when they bind to a specific structure of interest, can be used in PAINT microscopy. With such probes, background noise is reduced, because the probes that are diffusing within the buffer solution or within the sample but that have not been bound to the structure of interest do not emit appreciable fluorescence light. To achieve such probes, an enzyme that is genetically expressed can be tagged to a specific protein of interest, and then a PAINT probe that has a specific affinity for the enzyme and that becomes fluorescent only when bound to the enzyme could be used to emit fluorescence light in response to excitation light. In this manner, images of the specific protein of interest within a cell sample can be generated. The expression of the enzyme can be turned up to a high level to provide the density of binding sites for the PAINT probes, which is sufficiently great to provide super resolution images of the sample. Then, the density of the PAINT probes in the buffered solution can be controlled, so that fluorescence light from PAINT probes that bind to the enzymes can be individually resolved.

[0219] In some implementations, PAINT microscopy techniques can be combined with excitation of the PAINT probes by light sheets that are thin compared to the depth of focus of the detection objective to track single particles within a sample. For example, a sample can be pre-bleached fluorescence from molecules that might otherwise provide background noise, and then a sparse density of PAINT probes can be introduced to the sample and allowed to diffuse, or be transported, within the sample. The density of PAINT probes that are introduced to the sample can be low enough that fluorescence light from individual probes does not overlap on the detector so that the individual probes can be resolved. Then, by continuously scanning the light sheet and detection objective focal plane relative to the sample in the Z-axis direction or by continuously scanning the sample relative to the light sheet and detection objective focal plane, fluorescence light from individual PAINT probes can be detected. The individual PAINT probes can be localized in three dimensions and also in time based on the detected fluorescence light. Information about the four dimensional locations (i.e., three spatial dimensions plus one temporal dimension) of the PAINT probes can be used to generate a track of the PAINT probes as they move within the sample.

[0220] FIG. 36 is a schematic diagram of an optical system 3600 for providing thin light sheets to a sample that is imaged with at least PAINT techniques. A beam 3602 from an excitation laser 3604 is passed through X- and Z-cylindrical lenses 3606, 3608 to expand the beam that is provided to a wavefront modulating element (e.g., a binary spatial light modulator) 3610. The wavefront modulating element 3610 can be programmed to modulate the beam so that the beam that is provided to the sample 3612 has a thickness in the Z-axis direction that is thin compared to the depth of focus of the detection objective 3614. For example, the wavefront modulating element 3610 can be programmed so that the beam that is provided to the sample 3612 is a lattice light sheet or one or more Bessel-like beams. The beam(s) can be steered in the X- and Z-directions by an X-galvanometer 3616 and a Z-galvanometer 3618 and then provided to the sample through an excitation objective.

[0221] The sample can be located in a sample holder 3622 on a stage that can be moved (e.g. by a piezoelectric actuator), and the sample can be bathed in a buffer solution containing PAINT probes that have specific affinities for different structures on or within the sample. The solution containing the PAINT probes can be provided from a source 3624. Fluorescence light from the sample can be imaged by detection optics that include the detection objective 3614 that has a depth of focus that is comparable to or greater than the thickness of the excitation light sheet. Fluorescence light can be imaged onto a detector (e.g., a camera), and the fluorescent light signals on the detector can be analyzed by a computing device. The system also can include an Epi objective 3628 that can both provide excitation light to, and image fluorescence light from, the sample. The optical elements of the system 3600 can be controlled by a one or more computer systems and/or processors 3630, and the data acquired by the camera 3626 can be processed by one or more computer systems and/or processors 3630.

[0222] By limiting the illumination volume and providing high labeling density, PAINT microscopy using thin sheets of excitation light allows for sub-100 nm resolution imaging of thick 3D specimens including dividing cells and at the periphery of small embryos. Due to the stochastic nature of localization microscopy, obtaining sufficient localization density to resolve a given spatial frequency can require a several fold increase in the number of individual molecules compared to what is strictly required according to the Nyquist criteria. It also illustrates the limitations of using the localizations of a specific protein as a surrogate to resolve an underlying structure within which the protein resides. Unfortunately, for many proteins, endogenous expression levels may not support sampling of an underlying structure at high spatial resolution, even if every protein molecule of a specific type in a region of interest could be labeled and localized. This may explain why localization microscopy datasets are largely limited to a few prototypical structural proteins that are normally expressed at or locally condensed at very high densities such as cytoskeletal components (actin, tubulin), focal adhesions (vinculin, paxillin) or endocytic pits (clathrin, caveolin). It also suggests that PAINT labels targeted to lipids can enable higher resolution than localization microscopy techniques that target a specific protein, and may point out an intrinsic limitation of protein engineering that would be shared even by electron microscopy (EM) methods utilizing protein-specific contrast.

[0223] A corollary of this is that the need for high localization density over a large 3D volume requires an enormous number of localization events that require substantial time to acquire. For example, datasets used to create sample images may includes of over 100,000 3D volumes, each including approximately 100 2D image planes. At 25 ms exposure per image, this translates to a volumetric imaging rate of 0.4 Hz, resulting in a total imaging duration of approximately 69 hours.

[0224] In PAINT microscopy of 3D specimens, the diffusion rate of the label into the sample can be rate limiting at a certain depth. Faster imaging with higher intensity excitation light can increase the probability that these labels bleach before they reach their targets within the interior portions of the sample, away from the cellular periphery. Even when imaging at 0.4 Hz, images of relatively large 3D specimens can show decreasing numbers of localizations proportional to the distance from the cell surface. Although increasing the illumination intensity, decreasing the exposure per image, or utilizing multi-emitter fitting algorithms can decrease the time required to attain a single volume, the upper bound on volumetric imaging rate can be fixed by the sample thickness and dye properties. Nevertheless, throughput can be improved by imaging multiple regions of a sample, or multiple different samples, per coverslip in a single experiment.

[0225] Because the localization density decreases with depth, care must be taken when interpreting PAINT microscopy results. Specifically, one must consider that in the super-resolved image, contrast is proportional to the density of stable binding sites in the sample multiplied by a concentration gradient of fluorescent molecules generated by diffusion of unbleached labels from the imaging solution into the sample. This may be especially important when imaging very dense regions such as tightly packed heterochromatin in the cell nucleus. If quantitative counting of binding sites is required, the label concentration gradient could be estimated from the bulk concentration and by using molecules that are localized in sequential frames to report local diffusion rates within the sample.

[0226] In addition new PAINT labels that can be targeted to different sub-cellular structures can be beneficial. For example, protein specific contrast has been demonstrated for PAINT-specific DNA oligomers attached to antibodies, but the localization density is then limited by the initial immunolabeling density, which is generally low. Development of direct-binding labels for PAINT microscopy is challenging for several reasons. First, in the conventional process where labels are introduced prior to imaging, the image contrast is proportional to the ratio of the specific to non-specific binding constants (where Kspecific=kon-specific/koff-specific and Knonspecific=kon-nonspecific/koff-nonspecific). However, because localization and subsequent photobleaching in PAINT can occur very shortly after the molecule binds to the substrate, PAINT image contrast can be predominantly proportional to the on-rate ratios of kon-specific to kon-nonspecific which can be harder to optimize than koff. Fluorogenic ligands, such as those based on environmentally sensitive JF64614 could render nonspecific binding events invisible, effectively increasing kon-specific.

[0227] Second, rapid diffusion within both the solution and the sample of PAINT probe is enhanced by using smaller probes, but conferring binding specificity while maintaining the small size of the label can be difficult. To address this, proteins or protein fragments that are known to have inherent binding activity to specific sub-cellular structures can be screened to generate several new PAINT probes that are targeted to specific cytoskeletal filaments (actin, microtubules, or intermediate filaments) or to focal adhesions. Alternatively, further development of fluorogenic drug-dye conjugates can expand the palette of PAINT probes to other proteins. In addition, using gene editing techniques such as CRISPR (clustered regularly interspaced short palindromic repeats) to express endogeneous levels of a target protein conjugated with 100% efficiency to a genetically-encoded self-labeling tag such as Snap-tag or HaloTag that serves as the target for a fluorescently labeled PAINT ligand. Indeed, this method has worked well for live-cell single molecule tracking and mapping of transcription factor binding sites.

[0228] Implementations of the various techniques described herein may be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. Implementations may implemented as a computer program product, i.e., a computer program tangibly embodied in an information carrier, e.g., in a machine-readable storage device or in a propagated signal, for execution by, or to control the operation of, data processing apparatus, e.g., a programmable processor, a computer, or multiple computers. A computer program, such as the computer program(s) described above, can be written in any form of programming language, including compiled or interpreted languages, and can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network.

[0229] Method steps may be performed by one or more programmable processors executing a computer program to perform functions by operating on input data and generating output. Method steps also may be performed by, and an apparatus may be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit).

[0230] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. Elements of a computer may include at least one processor for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer also may include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory may be supplemented by, or incorporated in special purpose logic circuitry.

[0231] To provide for interaction with a user, implementations may be implemented on a computer having a display device, e.g., a cathode ray tube (CRT) or liquid crystal display (LCD) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.